Heater pattern including heaters powered by wind-electricity for in situ thermal processing of a subsurface hydrocarbon-containing formation

ABSTRACT

Some embodiments of the present invention relate to the use of wind-electricity to produce unconventional oil from a kerogen-containing or bitumen-containing subsurface formation. A heater cell may be divided into nested inner and outer zones. In the smaller inner zone, heaters may be arranged at a relatively high spatial density while in the larger surrounding outer zone, a heater spatial density may be significantly lower. Due to the higher heater density, a rate of temperature increase in the smaller inner zone of the subsurface exceeds that of the larger outer zone, and a rate of hydrocarbon fluid production ramps up faster in the inner zone than in the outer zone. In some embodiments, at least a majority of the heaters in the inner zone are powered primarily by fuel combustion and at least a majority of heaters in the outer zone are powered primarily by electricity generated by wind. Alternatively, in other embodiments, at least a majority of the heaters in the inner zone are powered primarily by electricity generated by wind and at least a majority of heaters in the outer zone are powered primarily by fuel combustion.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of PCT/US13/38089 filed onApr. 24, 2013. This application claims priority to U.S. 61/729,628 filedon Nov. 25, 2012.

FIELD OF THE INVENTION

The present invention relates to methods and systems of heating asubsurface formation, for example, in order to produce hydrocarbonfluids therefrom.

DESCRIPTION OF RELATED ART

Hydrocarbons obtained from subterranean formations are often used asenergy resources, as feedstocks, and as consumer products. Concerns overdepletion of available hydrocarbon resources and concerns over decliningoverall quality of produced hydrocarbons have led to development ofprocesses for more efficient recovery, processing and/or use ofavailable hydrocarbon resources. In situ processes may be used to removehydrocarbon materials from subterranean formations that were previouslyinaccessible and/or too expensive to extract using available methods.Chemical and/or physical properties of hydrocarbon material in asubterranean formation may need to be changed to allow hydrocarbonmaterial to be more easily removed from the subterranean formationand/or increase the value of the hydrocarbon material. The chemical andphysical changes may include in situ reactions that produce removablefluids, composition changes, solubility changes, density changes, phasechanges, and/or viscosity changes of the hydrocarbon material in theformation.

Large deposits of heavy hydrocarbons (heavy oil and/or tar) contained inrelatively permeable formations (for example in tar sands) are found inNorth America, South America, Africa, and Asia. Tar can be surface-minedand upgraded to lighter hydrocarbons such as crude oil, naphtha,kerosene, and/or gas oil. Surface milling processes may further separatethe bitumen from sand. The separated bitumen may be converted to lighthydrocarbons using conventional refinery methods. Mining and upgradingtar sand is usually substantially more expensive than producing lighterhydrocarbons from conventional oil reservoirs.

Retorting processes for oil shale may be generally divided into twomajor types: aboveground (surface) and underground (in situ).Aboveground retorting of oil shale typically involves mining andconstruction of metal vessels capable of withstanding high temperatures.The quality of oil produced from such retorting may typically be poor,thereby requiring costly upgrading. Aboveground retorting may alsoadversely affect environmental and water resources due to mining,transporting, processing, and/or disposing of the retorted material.Many U.S. patents have been issued relating to aboveground retorting ofoil shale. Currently available aboveground retorting processes include,for example, direct, indirect, and/or combination heating methods.

In situ retorting typically involves retorting oil shale withoutremoving the oil shale from the ground by mining. Modified in situprocesses typically require some mining to develop underground retortchambers. An example of a “modified” in situ process includes a methoddeveloped by Occidental Petroleum that involves mining approximately 20%of the oil shale in a formation, explosively rubblizing the remainder ofthe oil shale to fill up the mined out area, and combusting the oilshale by gravity stable combustion in which combustion is initiated fromthe top of the retort. Other examples of “modified” in situ processesinclude the “Rubble In Situ Extraction” (“RISE”) method developed by theLawrence Livermore Laboratory (“LLL”) and radio-frequency methodsdeveloped by IIT Research Institute (“IITRI”) and LLL, which involvetunneling and mining drifts to install an array of radio-frequencyantennas in an oil shale formation.

Obtaining permeability in an oil shale formation between injection andproduction wells tends to be difficult because oil shale is oftensubstantially impermeable. Drilling such wells may be expensive and timeconsuming. Many methods have attempted to link injection and productionwells.

Many different types of wells or wellbores may be used to treat thehydrocarbon-containing formation using an in situ heat treatmentprocess. In some embodiments, vertical and/or substantially verticalwells are used to treat the formation. In some embodiments, horizontalor substantially horizontal wells (such as J-shaped wells and/orL-shaped wells), and/or U-shaped wells are used to treat the formation.In some embodiments, combinations of horizontal wells, vertical wells,and/or other combinations are used to treat the formation. In certainembodiments, wells extend through the overburden of the formation to ahydrocarbon-containing layer of the formation. In some situations, heatin the wells is lost to the overburden. In some situations, surface andoverburden infrastructures used to support heaters and/or productionequipment in horizontal wellbores or U-shaped wellbores are large insize and/or numerous.

Wellbores for heater, injection, and/or production wells may be drilledby rotating a drill bit against the formation. The drill bit may besuspended in a borehole by a drill string that extends to the surface.In some cases, the drill bit may be rotated by rotating the drill stringat the surface. Sensors may be attached to drilling systems to assist indetermining direction, operating parameters, and/or operating conditionsduring drilling of a wellbore. Using the sensors may decrease the amountof time taken to determine positioning of the drilling systems. Forexample, U.S. Pat. No. 7,093,370 to Hansberry and U.S. PatentApplication Publication No. 2009-027041 to Zaeper et al, both of whichare incorporated herein by reference, describe a borehole navigationsystems and/or sensors to drill wellbores in hydrocarbon formations. Atpresent, however, there are still many hydrocarbon-containing formationswhere drilling wellbores is difficult, expensive, and/or time consuming.

Heaters may be placed in wellbores to heat a formation during an in situprocess. There are many different types of heaters which may be used toheat the formation. Examples of in situ processes utilizing downholeheaters are illustrated in U.S. Pat. No. 2,634,961 to Ljungstrom; U.S.Pat. No. 2,732,195 to Ljungstrom; U.S. Pat. No. 2,780,450 to Ljungstrom;U.S. Pat. No. 2,789,805 to Ljungstrom; U.S. Pat. No. 2,923,535 toLjungstrom; U.S. Pat. No. 4,886,118 to Van Meurs et al.; and U.S. Pat.No. 6,688,387 to Wellington et al.; each of which is incorporated byreference as if fully set forth herein.

As discussed above, there has been a significant amount of effort todevelop methods and systems to economically produce hydrocarbons,hydrogen, and/or other products from hydrocarbon-containing formations.At present, however, there are still many hydrocarbon-containingformations from which hydrocarbons, hydrogen, and/or other productscannot be economically produced. Thus, there is a need for improvedmethods and systems for heating of a hydrocarbon formation andproduction of fluids from the hydrocarbon formation. There is also aneed for improved methods and systems that reduce energy costs fortreating the formation, reduce emissions from the treatment process,facilitate heating system installation, and/or reduce heat loss to theoverburden as compared to hydrocarbon recovery processes that utilizesurface based equipment.

SUMMARY OF EMBODIMENTS

Embodiments of the present invention relate to heater patterns andrelated methods of producing hydrocarbon fluids from a subsurfacehydrocarbon-containing formation (for example, an oil shale formation)where a heater cell may be divided into nested inner and outer zones.One or more heaters of the heater cell are powered primarily byelectricity generated by wind. Production wells may be located withinone or both zones. In the smaller inner zone, heaters are arranged at arelatively high spatial density while in the larger surrounding outerzone, a heater spatial density is significantly lower. Due to the higherheater density, a rate of temperature increase in the smaller inner zoneof the subsurface exceeds that of the larger outer zone, and a rate ofhydrocarbon fluid production ramps up significantly faster in the innerzone than in the outer zone.

The overall density of heaters in the heater cell, considered as awhole, is significantly less than that within the inner zone. Thus, thenumber of heaters required for the heater pattern is substantially lessthan what would be required if the heater density throughout the heatercell was that within the inner zone.

In a first embodiment related to heater patterns and wind electricity,at least a majority (in some embodiments, at least two-thirds) ofheaters of the inner zone are powered primarily by wind electricitywhile at least a majority (in some embodiments, at least two-thirds) ofheaters of the outer zone are powered primarily by fuel combustion. Thismay be useful, for example, in remote locations with minimalinfrastructure where it is relatively easy to install wind turbinesdespite their expense. Almost immediately after installing the windturbines and associated inner-zone heaters, it is possible to commenceheating of at least the inner zone with minimal delay. At a later time,for example, when combustible pyrolysis gas from the inner zone isavailable or when appropriate infrastructure is available, it ispossible to rely on this pyrolysis gas or infrastructure (e.g. a powerplant) to supply energy to the outer zone heaters.

The second embodiment relates to the opposite situation. In the secondembodiment, (i) at least a majority (e.g. at least half, or at leasttwo-thirds) of heaters of the inner zone are powered primarily by fossilfuel electricity or by fossil fuel combustion and (ii) at least amajority (e.g. at least half, or at least two-thirds) of heaters of theouter zone are powered primarily by wind electricity. Because the outerzone heaters typically operate for a significantly longer period oftime, the second embodiment is particularly advantageous for minimizingCO₂ footprint. In the inner zone, a reliable/continuous energy source isimportant (i.e. rather than relying on intermittent wind or solar), soas to ensure early production of hydrocarbon production from theformation. In this second embodiment, most inner zone heaters thereforederive their power from fossil fuels as opposed to from intermittentsources. Thus ensures that the inner zone heats up quickly and minimizesa time delay before production begins.

In both of these embodiments, thermal energy from the inner zone maymigrate outwardly to the outer zone so as to accelerate hydrocarbonfluid production in the outer zone. Despite the significantly lowerheater density in the outer zone, a rate of hydrocarbon fluid productionin the outer zone may ramp up fast enough so that the overall rate ofhydrocarbon fluid production for the heater cell as a whole issubstantially sustained, over an extended period of time, once the innerzone production rate has peaked.

As such, the heater patterns disclosed herein provide the minimal, ornearly the minimal, rise time to a substantially sustained productionrate that is possible for a given number of heaters. Alternatively, itmay be said that the heater patterns disclosed herein minimize, ornearly minimize, the number of heaters required to achieve a relativelyfast rise time with a sustained production level.

In some embodiments, a heater spacing within the outer zone is abouttwice that of the inner zone and/or a heater density within the innerzone is about three times that of the outer zone and/or an averagedistance, in the inner zone, to a nearest heater is about 2-3 times thatwithin the outer zone. In some embodiments, an area of a region enclosedby a perimeter of the outer zone is between two and seven (e.g. at leasttwo or at least three and/or at most seven or at most six or at mostfive) times (for example, about four times) that enclosed by a perimeterof the inner zone.

In some embodiments, the inner zone, outer zone or both are shaped as aregular hexagon. This shape may be particularly useful when heater cellsare arranged on a two-dimensional lattice so as to fill atwo-dimensional portion of the subsurface while eliminating orsubstantially minimizing the size of the interstitial space betweenneighboring heater cells. As such, a number of heater cells mayentirely, or almost entirely, cover a portion of the sub-surface.

Some embodiments of the present invention relate to ‘two-level’ heaterpatterns where an inner zone of heaters at a higher density is nestedwithin an outer zone of heaters at a lower density. This concept may begeneralized to N-level heater patterns where one or more ‘outer’ zonesof heaters surround a relatively heater-dense inner zone of heaters. Inone example, N=2. In another example, N=3. In yet another example, N=4.

For each pair of heater zones, the more outer heater zone is larger thanthe more inner heater zone. Although the heater density in the moreouter heater zone is significantly less than that in the more innerzone, and although the hydrocarbon fluid production peak in the innerzone occurs at a significantly earlier time than in the more outer zone,sufficient thermal energy is delivered to the more outer zone so oncethe production rate in the more inner zone ramps up quickly, this ratemay be substantially sustained for a relatively extended period of timeby hydrocarbon fluid production rate in the more outer zone.

In some embodiments, further performance improvements may be achievedby: (i) concentrating electrical heaters in the denser inner zone whilethe heaters of the outer zone are primarily molten salt heaters; and/or(ii) significantly reducing a power output of the inner-zone heaterafter an inner zone hydrocarbon fluid production rate has dropped (e.g.by a first minimal threshold fraction) from a maximum level; and/or(iii) substantially shutting off one or more inner zone production wellsafter the inner zone hydrocarbon fluid production rate has dropped (e.g.by a second minimal threshold fraction equal to or differing from thefirst minimal threshold fraction) from a maximum level; and/or (iv)injecting heat-transfer fluid into the inner zone (e.g. via inner zoneproduction well(s) and/or via inner zone injection well(s)) so as toaccelerate the outwardly migration of thermal energy from the inner zoneto the outer zone—for example, by supplementing outwardly-directeddiffusive heater transfer with outwardly-directed convective heattransfer.

It is now disclosed a system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that an average heater spacing in outer zonesignificantly exceeds that of inner zone, at least a majority of theheaters in the inner zone being powered primarily by fuel combustion andat least a majority of heaters in the outer zone being powered primarilyby electricity generated by wind.

It is now disclosed a system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that an average heater spacing in outer zonesignificantly exceeds that of inner zone, at least a majority of theheaters in the inner zone being powered primarily by fuel combustion andat least a majority of heaters in the outer zone being powered primarilyby electricity generated by wind.

It is now disclosed a system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that a heater spatial density in inner zone significantlyexceeds that of outer zone, at least a majority of the heaters in theinner zone being powered primarily by fuel combustion and at least a ofheaters in the outer zone being powered primarily by electricitygenerated by wind.

It is now disclosed a system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: heaters arranged in a target portion of the formation, thetarget portion being divided into nested inner and outer zones heatersso that inner zone and outer zone heaters are respectively distributedaround inner and outer zone centroids, at least a majority of theheaters in the inner zone being powered primarily by fuel combustion andat least a majority of heaters in the outer zone being powered primarilyby electricity generated by wind.

It is now disclosed a system for in-situ production of hydrocarbonfluids from a subsurface formation, the system comprising: (i) heaterspowered primarily by fuel combustion and (ii) heaters powered primarilyby electricity generated by wind arranged within a target portion of thesub-surface formation.

In some embodiments, within the target formation, a first heater that ispowered primarily by fuel combustion is located at most 50 meters from asecond heater that is powered primarily by electricity generated bywind.

In some embodiments, within the target formation, a first heater that ispowered primarily by fuel combustion is located at most 35 meters from asecond heater that is powered primarily by electricity generated bywind.

In some embodiments, within the target formation, a first heater that ispowered primarily by fuel combustion is located at most 20 meters from asecond heater that is powered primarily by electricity generated bywind.

In some embodiments, within the target formation, a first heater that ispowered primarily by fuel combustion is located at most 10 meters from asecond heater that is powered primarily by electricity generated bywind.

In some embodiments, within the target formation, a first heater that ispowered primarily by fuel combustion is located at most 5 meters from asecond heater that is powered primarily by electricity generated bywind.

In some embodiments, within the target formation, the average separationdistance between neighboring heaters that are each powered primarily byelectricity generated by wind exceeds the average separation distancebetween neighboring heaters that are each powered primarily by fuelcombustion.

In some embodiments, within the target formation, the average separationdistance between neighboring heaters that are each powered primarily byelectricity generated by wind significantly exceeds the averageseparation distance between neighboring heaters that are each poweredprimarily by fuel combustion.

In some embodiments, within the target formation, the average separationdistance between neighboring heaters that are each powered primarily byelectricity generated by wind significantly is about twice the averageseparation distance between neighboring heaters that are each poweredprimarily by fuel combustion.

In some embodiments, at least some, or at least a majority, or at leasttwo-thirds of the heaters powered primarily by fuel combustion areelectrical heaters that are powered primarily by electricity generatedby fuel combustion.

In some embodiments, at least some, or at least a majority, or at leasttwo-thirds of the heaters powered primarily by fuel combustion arecombustion heaters where a combusted gas circulated in the subsurface.

In some embodiments, at least some, or at least a majority, or at leasttwo-thirds of the heaters powered primarily by fuel combustion areelectrical heaters wherein a material is resistively heated byelectricity generated by fuel combustion.

In some embodiments, at least some, or at least a majority, or at leasttwo-thirds of the heaters powered primarily by fuel combustion areadvection heaters where a material, that is in thermal communicationwith a circulating heat transfer fluid flowing in the subsurface, isheated resistively by electricity generated by fuel combustion.

In some embodiments, the resistively heated material is in thesubsurface.

In some embodiments, the resistively heated material is above thesurface.

In some embodiments, at least some, or at least a majority, or at leasttwo-thirds of the heaters powered primarily by electricity generated bywind are electrical heaters wherein a material is resistively heated byelectricity generated by wind.

In some embodiments, at least some, or at least a majority, or at leasttwo-thirds of the heaters powered primarily by electricity generated bywind are advection heaters where a material, that is in thermalcommunication with a circulating heat transfer fluid flowing in thesubsurface, is heated resistively by electricity generated by wind.

In some embodiments, the resistively heated material is in thesubsurface.

In some embodiments, the resistively heated material is above thesurface.

In some embodiments, wherein two-thirds of the heaters in the inner zoneare powered primarily by fuel combustion and at least two-thirds ofheaters in the outer zone being powered primarily by electricitygenerated by wind.

It is now disclosed a method of in-situ production of hydrocarbon fluidsin a subsurface hydrocarbon-containing formation, the method comprising:a. during an earlier stage of production, producing hydrocarbon fluidsprimarily in a first portion of the target region that is heatedprimarily by thermal energy derived from combustion of fuel; and b.during a later stage of production, producing hydrocarbon fluidprimarily in a second portion of the target region that is heatedprimarily by thermal energy derived from electricity generated by wind,wherein at least some of the thermal energy required for hydrocarbonfluid production in the second portion of the target region is suppliedby outward migration of thermal energy from the first portion to thesecond portion of the target region.

It is now disclosed a method of in-situ production of hydrocarbon fluidsin a subsurface hydrocarbon-containing formation, the method comprising:a. during an earlier stage of production, producing hydrocarbon fluidsprimarily in a first portion of the target region that is heatedprimarily by thermal energy derived from electricity generated by windand b. during a later stage of production, producing hydrocarbon fluidprimarily in a second portion of the target region that is heatedprimarily by thermal energy derived from combustion of fuel wherein atleast some of the thermal energy required for hydrocarbon fluidproduction in the second portion of the target region is supplied byoutward migration of thermal energy from the first portion to the secondportion of the target region.

It is now disclosed a system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that an average heater spacing in outer zonesignificantly exceeds that of inner zone, at least a majority of theheaters in the inner zone being powered primarily by electricitygenerated by wind and at least a majority of heaters in the outer zonebeing powered primarily by fuel combustion.

It is now disclosed a system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that an average heater spacing in outer zonesignificantly exceeds that of inner zone, at least a majority of theheaters in the inner zone being powered primarily by electricitygenerated by wind and at least a majority of heaters in the outer zonebeing powered primarily by fuel combustion.

It is now disclosed a system for system for in-situ production ofhydrocarbon fluids from a subsurface hydrocarbon-containing formation,the system comprising: a heater cell divided into nested inner and outerzones such that an enclosed area ratio between respective areas enclosedby substantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that a heater spatial density in inner zone significantlyexceeds that of outer zone, at least a majority of the heaters in theinner zone being powered primarily by electricity generated by wind andat least a majority of heaters in the outer zone being powered primarilyby fuel combustion.

It is now disclosed a system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: heaters arranged in a target portion of the formation, thetarget portion being divided into nested inner and outer zones heatersso that inner zone and outer zone heaters are respectively distributedaround inner and outer zone centroids, at least a majority of theheaters in the inner zone being powered primarily by electricitygenerated by wind and at least a majority of heaters in the outer zonebeing powered primarily by fuel combustion.

In some embodiments, at least two-thirds of the heaters in the innerzone are powered primarily by electricity generated by wind and at leasttwo-thirds of heaters in the outer zone being powered primarily by fuelcombustion.

In some embodiments, a centroid of the inner zone is located in acentral portion of the region enclosed by a perimeter of the outer zone.In some embodiments, each heater cell includes at least one productionwell located within the inner zone. In some embodiments, each heatercell includes at least one production well located within the outerzone. In some embodiments, a production well spatial density in theinner zone at least exceeds that of the outer zone. In some embodiments,an average heater spacing in outer zone is at least about twice that ofinner zone. In some embodiments, the area ratio between respective areasenclosed by inner zone and outer zone perimeters is about four, and anaverage heater spacing in the outer zone is about twice that of theinner zone. In some embodiments, a spacing ratio between an averageheater spacing of the outer zone and that of the inner zone is aboutequal to a square root of the area ratio between respective areasenclosed by the inner zone and outer zone perimeters. In someembodiments, a spacing ratio between an average heater spacing of theouter zone and that of the inner zone is about equal to a square root ofthe area ratio between respective areas enclosed by inner zone and outerzone perimeters. In some embodiments, a heater spatial density in theinner zone is at least about twice that of outer zone. In someembodiments, a heater spatial density in the inner zone is at leasttwice that of the outer zone. In some embodiments, a heater spatialdensity in the inner zone is at least about three times that of theouter zone. In some embodiments, a heater density ratio between a heaterspatial densities in the inner zone and that of outer zone issubstantially equal to an area ratio between an area of the outer zoneand that of the inner zone.

In some embodiments, for an area ratio between an area enclosed by aperimeter of outer zone to that enclosed by a perimeter of inner zone isat most six or at most five and/or at least 3.5

In some embodiments, the one or more heater cells include first andsecond heater cells having substantially the same area and sharing atleast one common heater-cell-perimeter heater.

In some embodiments, the one or more heater cells further includes athird heater cell having substantially the same area as the first andsecond heater cells, the third heater cell sharing at least one commonheater-cell-perimeter heater with the first heater cell, the second andthird heater cells located substantially on opposite sides of the firstheater cell.

In some embodiments, a given heater cell of the heater cells issubstantially surrounded by a plurality of neighboring heater cells.

In some embodiments, a given heater cell of the heater cells issubstantially surrounded by a plurality of neighboring heater cells andthe given heater cell shares a common heater-cell-perimeter heater witheach of the neighboring heater cells.

In some embodiments, inner zone heaters are distributed substantiallyuniformly throughout the inner zone.

In some embodiments, each heater cell being arranged so that within theouter zone, heaters are predominantly located on the outer zoneperimeter.

In some embodiments, at least one of the inner and outer perimeters isshaped like a regular hexagon, like a lozenge, or like a rectangle.

In some embodiments, the inner and outer perimeters are similar shaped.

In some embodiments, within the inner and/or outer zones, a majority ofheaters are disposed on a triangular, hexagonal or rectangular grid.

In some embodiments, a total number of inner zone heaters exceeds thatof the outer zone.

In some embodiments, a total number of inner zone heaters exceeds thatof the outer zone by at least 50%.

In some embodiments, at least five inner zone heaters are dispersedthroughout the inner zone.

In some embodiments, at least five or at least seven or at least tenouter zone heaters are located around a perimeter of the outer zone.

In some embodiments, at least one-third of at least one-half of innerzone heaters are not located on the inner zone perimeter.

In some embodiments, for each of the inner zone and outer zoneperimeters, an aspect ratio is less than 2.5.

In some embodiments, at least five or at least seven or at least tenheaters are distributed about the perimeter of the inner zone.

In some embodiments, a majority of the heaters in the inner zone areelectrical heaters and a majority of the heaters in the outer zone aremolten salt heaters.

In some embodiments, at least two-thirds or at least three-quarters ofinner-zone heaters are electrical heaters and at least two-thirds ofouter-zone heaters are molten salt heaters.

In some embodiments, the system further includes control apparatusconfigured to regulate heater operation times so that, on average,heaters in the outer zone operate above a one-half maximum power levelfor at least twice as long as the heaters in the inner zone.

In some embodiments, the control apparatus is configured so that onaverage, the outer zone heaters operate above a one-half maximum powerlevel for at least three times as long as the inner zone heaters.

In some embodiments, an average inner-zone heater spacing is between 1and 10 meters (for example, between 1 and 5 meters or between 1 and 3meters).

In some embodiments, the heaters are configured to pyrolize the entiretyof both the inner and outer zones.

In some embodiments, the heaters are configured to heat respectivesubstantial entirety of the inner and outer regions to substantially thesame uniform temperature.

In some embodiments, among the inner zone heaters and/or outer zoneheaters and/or inner perimeter heaters and/or outer perimeter heaters, aratio between a standard deviation of the spacing and an average spacingis at most 0.2.

In some embodiments, all heaters have substantially the same maximumpower level and/or substantially the same diameter.

In some embodiments, a ratio between the area of the inner zone and asquare of an average distance to a nearest heater within the inner zoneis at least 80.

In some embodiments, a ratio between the area of the inner zone and asquare of an average distance to a nearest heater within the inner zoneis at least 60 or at least 70 or at least 80 or at least 90 or at least100.

In some embodiments, inner and outer zones respective havepolygon-shaped perimeters, such that heaters are located at all polygonvertices of inner and outer zone perimeters.

In some embodiments, the inner zone is substantially-convex.

In some embodiments, the outer zone is substantially-convex.

In some embodiments, an average heater spacing in the outer zonesignificantly exceeds that of the inner zone.

In some embodiments, an average heater spacing in the outer zone isabout twice that of the inner zone.

In some embodiments, a spacing ratio between an average heater spacingof the outer zone and that of the inner zone is about equal to a squareroot of the area ratio between respective areas enclosed by the innerzone and outer zone perimeters.

In some embodiments, a heater spatial density in inner zonesignificantly exceeds that of the outer zone.

In some embodiments, wherein a heater spatial density in the inner zoneis at least twice that of the outer zone.

In some embodiments, a heater spatial density in inner zone is at leastabout three times that of the outer zone.

In some embodiments, a heater density ratio between a heater spatialdensities in inner that of outer zones is substantially equal to a zonearea ratio between an area of outer zone and that of inner zone.

In some embodiments, an average distance to a nearest heater within theouter zone significantly exceeds that of the inner zone.

In some embodiments, an average distance to a nearest heater within theouter zone is between two and three times that of the inner zone.

In some embodiments, an average distance to a nearest heater on aperimeter of the inner zone is at most substantially equal to thatwithin inner zone.

In some embodiments, an average distance to a nearest heater on theouter zone perimeter is equal to at most about twice that on the innerzone perimeter.

In some embodiments, the system further comprises at least one innerzone production well within inner zone and at least one outer zoneproduction well within outer zone.

In some embodiments, a production well spatial density in inner zoneexceeds that of outer zone.

In some embodiments, a production well spatial density in inner zone isequal to about three times of outer zone.

In some embodiments, a majority of the outer zone heaters are arrangedon a perimeter of the outer zone.

In some embodiments, heaters are located at all polygon vertices ofinner and outer zone perimeters.

In some embodiments, heaters are located at all vertices of the OZSadditional zone perimeter.

In some embodiments, an average distance to a nearest heater within theouter zone is equal to between about two and about three times that ofthe inner zone.

In some embodiments, an average distance to a nearest heater within theouter zone is equal to between two and three times that of the innerzone.

In some embodiments, for each of the zone pairs, a heater spacing of themore outer zone is at least about twice that of the more inner zone.

In some embodiments, for each of the zone pairs, the area ratio betweenrespective more outer and more inner zones is about four, and a heaterspacing of the more outer zone is about twice that of the more innerzone.

In some embodiments, for each of the zone pairs, ratio between a heaterspacing of the more outer zone and that of the more inner zone issubstantially equal to square root of the area ratio between the moreouter and the more inner zones of the zone pair.

In some embodiments, for each of the zone pairs, the area ratio betweenrespective areas enclosed by perimeters of the more outer zone and themore inner zone is at most six.

In some embodiments, for each of the zone pairs, the area ratio betweenrespective areas enclosed by perimeters of the more outer zone and themore inner zone is at most five.

In some embodiments, for each of the zone pairs, the area ratio betweenrespective areas enclosed by perimeters of the more outer zone and themore inner zone is at least 2.5.

In some embodiments, a significant majority of the inner zone heatersare located away from outer zone perimeter.

In some embodiments, a significant majority of the outer zone heatersare located away from a perimeter of outer-zone-surrounding (OZS)additional zone.

In some embodiments, for each of the zone pairs, a heater spatialdensity of the more inner zone is equal to at least about twice that ofthe more outer zone.

In some embodiments, for each of the zone pairs, a heater spatialdensity of the more inner zone is equal to at most about six times thatof the more outer zone.

In some embodiments, for each of the zone pairs, a centroid of the moreinner zone is located in a central portion of the region enclosed by aperimeter of the more outer zone.

In some embodiments, for each of the zone pairs, an average distance toa nearest heater in the more outer zone is between about two and aboutthree times that of the less outer zone.

In some embodiments, for each of the zone pairs, an average distance toa nearest heater in the more outer zone is between two and three timesthat of the less outer zone.

In some embodiments, a centroid of inner zone is located in a centralportion of the region enclosed by a perimeter of the outer zone.

In some embodiments, the heater cell includes at least one inner zoneproduction well located within the inner zone.

In some embodiments, the heater cell includes at least one outer zoneproduction well located within the outer zone.

In some embodiments, the heater cell includes first and second outerzone production wells located within and on substantially on oppositesides of the outer zone.

In some embodiments, a production well spatial density in the inner zoneat least exceeds that of the outer zone.

In some embodiments, an average heater spacing in outer zone is at leastabout twice that of inner zone.

In some embodiments, the area ratio between respective areas enclosed byinner zone and outer zone perimeters, is about four, and an averageheater spacing in outer zone is about twice that of inner zone.

In some embodiments, a spacing ratio between an average heater spacingof the outer zone and that of the inner zone is about equal to a squareroot of the area ratio between respective areas enclosed by the innerzone and outer zone perimeters.

In some embodiments, a spacing ratio between an average heater spacingof the outer zone and that of the inner zone is about equal to a squareroot of the area ratio between respective areas enclosed by inner zoneand outer zone perimeters.

In some embodiments, a heater spatial density in inner zone is at leastabout twice that of outer zone.

In some embodiments, a heater spatial density in inner zone is at leasttwice that of outer zone.

In some embodiments, a heater spatial density in inner zone is at leastabout three times that of the outer zone.

In some embodiments, a heater density ratio between a heater spatialdensities in inner that of outer zones is substantially equal to a zonearea ratio between an area of outer zone and that of inner zone.

In some embodiments, an enclosed area ratio between an area enclosed bya perimeter of outer zone to that enclosed by a perimeter of inner zoneis at most six or at most five and/or at least 2.5 or at least three orat least three.

In some embodiments, an average distance to a nearest heater in theouter zone is between about two and about three times that of the innerzone.

In some embodiments, an average distance to a nearest heater in theouter zone is between two and three times that of the inner zone.

In some embodiments, an average distance to a nearest heater on theinner zone perimeter is substantially equal to that within inner zone.

In some embodiments, along the perimeter of outer zone, an averagedistance to a nearest heater is at most four times that along theperimeter of inner zone.

In some embodiments, along the perimeter of outer zone, an averagedistance to a nearest heater is at most three times that along theperimeter of inner zone.

In some embodiments, along the perimeter of outer zone, an averagedistance to a nearest heater is at most about twice that along theperimeter of inner zone.

In some embodiments, among outer-perimeter heaters located on theperimeter of outer zone, an average distance to a nearest heatersignificantly exceeds that among inner-perimeter heaters located on theperimeter of inner zone.

In some embodiments, among outer-perimeter heaters located on theperimeter of outer zone, an average distance to a second nearest heatersignificantly exceeds that among inner-perimeter heaters located on theperimeter of inner zone.

In some embodiments, the system includes a plurality of the heatercells, first and second of the heater cells having substantially thesame area and sharing at least one common heater-cell-perimeter heater.

In some embodiments, wherein a third of the heater cells hassubstantially the same area as the first and second heater cells, thethird heater cell sharing at least one common heater-cell-perimeterheater with the first heater cell, the second and third heater cellslocated substantially on opposite sides of the first heater cell.

In some embodiments, the system includes a plurality of the heatercells, at least one of which is substantially surrounded by a pluralityof neighboring heater cells.

In some embodiments, a given heater cell of the heater cells issubstantially surrounded by a plurality of neighboring heater cells andthe given heater cell 608 shares a common heater-cell-perimeter heaterwith each of the neighboring heater cells.

In some embodiments, inner zone heaters are distributed substantiallyuniformly throughout inner zone.

In some embodiments, the heater cell is arranged so that within theouter zone, heaters are predominantly located on the outer zoneperimeter.

In some embodiments, at least one of the inner and outer perimeters isshaped like a regular hexagon, like a lozenge, or like a rectangle.

In some embodiments, the inner and outer perimeters are like-shaped.

In some embodiments, within the inner and/or outer zones, a majority ofheaters are disposed on a triangular grid, hexagonal or rectangulargrid.

In some embodiments, a total number of inner zone heaters exceeds thatof the outer zone.

In some embodiments, a total number of inner zone heaters exceeds thatof the outer zone by at least 50%.

In some embodiments, at least five inner zone heaters are dispersedthroughout the inner zone.

In some embodiments, at least five or at least seven or at least tenouter zone heaters are located around a perimeter of outer zone.

In some embodiments, at least one-third of at least one-half of innerzone heaters are not located on inner zone perimeter.

In some embodiments, each of the inner zone and outer zone perimeters,has an aspect ratio equal to most 2.5.

In some embodiments, each of the inner zone and outer zone perimeters,has an aspect ratio equal to least 10.

In some embodiments, each of the inner zone and outer zone perimeters,is shaped like a rectangular.

In some embodiments, at least five or seven or nine heaters aredistributed about the perimeter of inner zone and/or about the perimeterof the outer zone.

In some embodiments, at least ten heaters are distributed throughoutinner zone.

In some embodiments, a majority of the heaters in inner zone areelectrical heaters and a majority of the heaters in outer zone aremolten salt heaters.

In some embodiments, at least two-thirds or at least three-quarters ofinner-zone heaters are electrical heaters and at least two-thirds ofouter-zone heaters are molten salt heaters.

In some embodiments, the system further includes control apparatusconfigured to regulate heater operation times so that, on average,heaters in outer zone operate above a one-half maximum power level forat least twice as long as the heaters in inner zone.

In some embodiments, the system includes control apparatus configured toregulate heater operation times so that, on average, outer zone heatersoperate above a one-half maximum power level for at least twice as longas the inner zone heaters.

In some embodiments, the control apparatus is configured so that onaverage, outer zone heaters operate above a one-half maximum power levelfor at least three times as long as the inner zone heaters.

In some embodiments, wherein an average inner-zone heater spacing is atmost 20 meters or at most 10 meters or at most 5 meters.

In some embodiments, an area of the inner zone is at most one squarekilometer.

In some embodiments, an area of the inner zone is at most 500 squaremeters.

In some embodiments, the heaters are configured to induce pyrolysisthroughout substantial entireties of both the inner and outer zones.

In some embodiments, the heaters are configured to heat respectivesubstantial entirety of the inner and outer regions to substantially thesame uniform temperature.

In some embodiments, among the inner zone heaters and/or outer zoneheaters and/or inner perimeter heaters and/or outer perimeter heaters, aratio between a standard deviation of the spacing and an average spacingis at most 0.2.

In some embodiments, all heaters have substantially the same maximumpower level and/or substantially the same diameter.

In some embodiments, a ratio between the area of the inner zone and asquare of an average distance to a nearest heater within the inner zoneis at least 80 or at least 70 or at least 60 or at least 90.

In some embodiments, at most 10% or at most 7.6% or at most 5% or atmost 4% or at most 3% of a length of the outer zone perimeter.

In some embodiments, an average distance to a nearest heater is at mostone-eighth or at most one-tenth or at most one-twelfth of a square rootof an area of the inner zone.

In some embodiments, at most 30% or at most 20% or at most 10% of theinner zone is displaced from a nearest heater by length threshold equalto at most one quarter of a square root of the inner zone.

In some embodiments, at most 10% of the inner zone is displaced from anearest heater by length threshold equal to at most one quarter of asquare root of the inner zone.

In some embodiments, the length threshold equals at most one fifth of asquare root of the inner zone.

In some embodiments, an aspect ratio of the inner and/or outer zone isat most four or most 3 or at most 2.5.

In some embodiments, among the inner and outer zones, a ratio between agreater aspect ratio and a lesser aspect ratio is at most 1.5.

In some embodiments, an isoperimetric quotient of perimeters, of theinner and/or outer zone is at least 0.4 or at least 0.5 or at least 0.6.

In some embodiments, a perimeter of inner zone has a convex shapetolerance value of at most 1.2 or at most 1.1.

In some embodiments, heaters are arranged within inner zone so thatinner zone heaters are present on every 72 degree sector or every 60degree sector thereof for any reference ray orientation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic view of an embodiment of a portion of the insitu heat treatment system for treating the hydrocarbon-containingformation.

FIGS. 2-3, 8-14, and 18-37 illustrate in-situ heater patterns inaccordance with various examples.

FIGS. 4-7 describe illustrative production functions for a two-levelheater cell.

FIGS. 15-17 illustrate various sub-surface heaters.

DETAILED DESCRIPTION OF EMBODIMENTS

For convenience, in the context of the description herein, various termsare presented here. To the extent that definitions are provided,explicitly or implicitly, here or elsewhere in this application, suchdefinitions are understood to be consistent with the usage of thedefined terms by those of skill in the pertinent art(s). Furthermore,such definitions are to be construed in the broadest possible senseconsistent with such usage.

The following description generally relates to systems and methods fortreating hydrocarbons in the formations. Such formations may be treatedto yield hydrocarbon products, hydrogen, and other products.

Unless specified otherwise, for the present disclosure, when twoquantities QUANT₁ and QUANT₂, are ‘about’ equal to each other or‘substantially equal’ to each other, the quantities are either exactlyequal, or a ‘quantity ratio’ between (i) the greater of the twoquantities MAX(QUANT₁, QUANT₂) and (ii) the lesser of the two quantitiesMIN(QUANT₁, QUANT₂) is at most 1.3. In some embodiments, this ratio isat most 1.2 or at most 1.1 or at most 1.05. In the present disclosure,‘about’ equal and ‘substantially equal’ are used interchangeably andhave the same meaning.

An ‘about-tolerance-parameter’ governs an upper bound of the maximumpermissible deviation between two quantities that are ‘about equal.’ The‘about-tolerance-parameter’ is defined as the difference between the‘quantity ratio’ defined in the previous paragraph and 1. Thus, unlessotherwise specified, a value of the ‘about-tolerance-parameter’ is0.3—i.e. the ‘quantity ratio’ of the previous paragraph is at most 1.3.In some embodiments, the ‘about-tolerance-parameter’ is 0.2 (i.e. the‘quantity ratio’ of the previous paragraph is at most 1.2 or 1.1 or1.05). It is noted that the ‘about-tolerance-parameter’ is a globalparameter—when the about tolerance parameter is X then all quantitiesthat are ‘about’ or ‘substantially’ equal to each other have a ‘quantityratio’ of about 1+X.

Unless specified otherwise, if heaters (or heater wells) are arranged“around” a centroid of a ‘candidate’ region (e.g. an inner or outer orouter-zone-surrounding (OZS) additional zone), then for every ‘referenceray orientation’ (i.e. orientation of a ray from an origin), heaters(i.e. centroids thereof in a cross-section of the subsurface formationin which a heater pattern is defined) are present within all fourquadrants (i.e. 90 degree sector) of the candidate region where the‘origin’ is defined by the centroid of the ‘candidate region.’ In someembodiments, heaters are present, for every ‘reference ray orientation,’within every 72 degree sector or on every 60 degree sector or on every45 sector of the ‘candidate region.’

If heaters (or heater wells) are arranged ‘around’ a perimeter of acandidate region, then they are arranged ‘around’ the centroid of thecandidate region and on a perimeter thereof.

An “aspect ratio” of a shape refers to a ratio between its longerdimension and its shorter dimension.

In the context of reduced heat output heating systems, apparatus, andmethods, the term “automatically” means such systems, apparatus, andmethods function in a certain way without the use of external control(for example, external controllers such as a controller with atemperature sensor and a feedback loop, PID controller, or predictivecontroller).

A “centroid” of an object or region refers to the arithmetic mean of allpoints within the object or region. Unless specified otherwise, the‘object’ or ‘region’ for which a centroid is specified or computedactually refers to a two-dimensional cross section of an object orregion (e.g. a region of the subsurface formation). A ‘centroid’ of a‘heater’ or of a heater well is a ‘centroid’ of its ‘cross section’ ofthe heater or the heater well—i.e. at a specific location. Unlessspecified otherwise, this cross section is in the plane in which a‘heater pattern’ (i.e. for heaters and/or heater wells) is defined.

An object or region is “convex” if for every pair of points within theregion or object, every point on the straight line segment that joinsthem is also within the region or object. A closed curve (e.g. aperimeter of a two-dimensional region) is ‘convex’ if the area enclosedby the closed curve is convex.

A heater ‘cross section’ may vary along its central axis. Unlessspecified otherwise, a heater ‘cross section’ is the cross section inthe plane in which a ‘heater pattern’ is defined. Unless specifiedotherwise, for a given heater pattern, the ‘cross sections’ of each ofthe heaters are all co-planar.

The term ‘displacement’ is used interchangeably with ‘distance.’

A ‘distance’ between a location and a heater is the distance between thelocation and a ‘centroid’ of the heater (i.e. a ‘centroid’ of the heatercross section in the plane in which a ‘heater pattern’ is defined). The‘distance between multiple heaters’ is the distance between theircentroids.

A “formation” includes one or more hydrocarbon-containing layers, one ormore non-hydrocarbon layers, an overburden, and/or an underburden.“Hydrocarbon layers” refer to layers in the formation that containhydrocarbons. The hydrocarbon layers may contain non-hydrocarbonmaterial and hydrocarbon material. The “overburden” and/or the“underburden” include one or more different types of impermeablematerials. For example, the overburden and/or underburden may includerock, shale, mudstone, or wet/tight carbonate. In some embodiments of insitu heat treatment processes, the overburden and/or the underburden mayinclude a hydrocarbon-containing layer or hydrocarbon-containing layersthat are relatively impermeable and are not subjected to temperaturesduring in situ heat treatment processing that result in significantcharacteristic changes of the hydrocarbon-containing layers of theoverburden and/or the underburden. For example, the underburden maycontain shale or mudstone, but the underburden is not allowed to heat topyrolysis temperatures during the in situ heat treatment process. Insome cases, the overburden and/or the underburden may be somewhatpermeable.

“Formation fluids” refer to fluids present in a formation and mayinclude pyrolyzation fluid, synthesis gas, mobilized hydrocarbons, andwater (steam). Formation fluids may include hydrocarbon fluids as wellas non-hydrocarbon fluids. The term “mobilized fluid” refers to fluidsin a hydrocarbon-containing formation that are able to flow as a resultof thermal treatment of the formation. “Produced fluids” refer to fluidsremoved from the subsurface formation.

A “heat source” is any system for providing heat to at least a portionof a formation substantially by conductive and/or radiative heattransfer. For example, a heat source may include electric heaters suchas an insulated conductor, an elongated member, and/or a conductordisposed in a conduit. A heat source may also include systems thatgenerate heat by burning a fuel external to or in a formation. Thesystems may be surface burners, downhole gas burners, flamelessdistributed combustors, and natural distributed combustors. In someembodiments, heat provided to or generated in one or more heat sourcesmay be supplied by other sources of energy. The other sources of energymay directly heat a formation, or the energy may be applied to atransfer medium that directly or indirectly heats the formation. It isto be understood that one or more heat sources that are applying heat toa formation may use different sources of energy. Thus, for example, fora given formation some heat sources may supply heat from electricresistance heaters, some heat sources may provide heat from combustion,and some heat sources may provide heat from one or more other energysources (for example, chemical reactions, solar energy, wind energy,biomass, or other sources of renewable energy). A chemical reaction mayinclude an exothermic reaction (for example, an oxidation reaction). Aheat source may also include a heater that provides heat to a zoneproximate and/or surrounding a heating location such as a heater well.

A “heater” is any system or heat source for generating heat in a well ora near wellbore region. Heaters may be, but are not limited to, electricheaters, burners (e.g. gas burners), pipes through which hot heattransfer fluid (e.g. molten salt or molten metal) flows, combustors thatreact with material in or produced from a formation, and/or combinationsthereof. Unless specified otherwise, a ‘heater’ includes elongateportion having a length that is much greater than cross-sectiondimensions. One example of a ‘heater’ is a ‘molten salt heater’ whichheats the subsurface formation primarily by heat convection betweenmolten salt flowing therein and the subsurface formation.

A ‘heater pattern’ describes relative locations of heaters in a plane ofthe subsurface formation.

“Heavy hydrocarbons” are viscous hydrocarbon fluids. Heavy hydrocarbonsmay include highly viscous hydrocarbon fluids such as heavy oil, tar,and/or asphalt. Heavy hydrocarbons may include carbon and hydrogen, aswell as smaller concentrations of sulfur, oxygen, and nitrogen.Additional elements may also be present in heavy hydrocarbons in traceamounts. Heavy hydrocarbons may be classified by API gravity. Heavyhydrocarbons generally have an API gravity below about 20°. Heavy oil,for example, generally has an API gravity of about 10-20°, whereas targenerally has an API gravity below about 10°. The viscosity of heavyhydrocarbons is generally greater than about 100 centipoise at 15° C.Heavy hydrocarbons may include aromatics or other complex ringhydrocarbons.

“Hydrocarbons” are generally defined as molecules formed primarily bycarbon and hydrogen atoms. Hydrocarbons may also include other elementssuch as, but not limited to, halogens, metallic elements, nitrogen,oxygen, and/or sulfur. Hydrocarbons may be, but are not limited to,kerogen, bitumen, pyrobitumen, oils, natural mineral waxes, andasphaltites. Hydrocarbons may be located in or adjacent to mineralmatrices in the earth. Matrices may include, but are not limited to,sedimentary rock, sands, silicilytes, carbonates, diatomites, and otherporous media. “Hydrocarbon fluids” are fluids that include hydrocarbons.Hydrocarbon fluids may include, entrain, or be entrained innon-hydrocarbon fluids such as hydrogen, nitrogen, carbon monoxide,carbon dioxide, hydrogen sulfide, water, and ammonia.

An “in situ conversion process” refers to a process of heating ahydrocarbon-containing formation from heat sources to raise thetemperature of at least a portion of the formation above a pyrolysistemperature so that pyrolyzation fluid is produced in the formation.

An “in situ heat treatment process” refers to a process of heating ahydrocarbon-containing formation with heat sources to raise thetemperature of at least a portion of the formation above a temperaturethat results in mobilized fluid, visbreaking, and/or pyrolysis ofhydrocarbon-containing material so that mobilized fluids, visbrokenfluids, and/or pyrolyzation fluids are produced in the formation.

For the present disclosure, an ‘isoperimeteric quotient’ of a closedcurve (e.g. polygon) is a ratio between: (i) the product of 4π and anarea closed by the closed curve; and (ii) the square of the perimeter ofthe closed curve.

“Kerogen” is a solid, insoluble hydrocarbon that has been converted bynatural degradation and that principally contains carbon, hydrogen,nitrogen, oxygen, and sulfur. Coal and oil shale are typical examples ofmaterials that contain kerogen. “Bitumen” is a non-crystalline solid orviscous hydrocarbon material that is substantially soluble in carbondisulfide. “Oil” is a fluid containing a mixture of condensablehydrocarbons.

When an inner zone heater or a point on inner zone perimeter is ‘locatedaway’ from a perimeter of an outer zone, this means that the ‘locatedaway’ inner zone heater (or the ‘located away inner zone perimeterpoint’) is displaced from the outer zone perimeter by at least athreshold distance. Unless otherwise specified, this ‘thresholddifference’ is at least one half of an inner zone average heaterspacing.

“Production” of a hydrocarbon fluid refers to thermally generating thehydrocarbon fluid (e.g. from kerogen or bitumen) and removing the fluidfrom the sub-surface formation via a production well.

“Pyrolysis” is the breaking of chemical bonds due to the application ofheat. For example, pyrolysis may include transforming a compound intoone or more other substances by heat alone. Heat may be transferred to asection of the formation to cause pyrolysis.

“Pyrolyzation fluids” or “pyrolysis products” refers to fluid producedsubstantially during pyrolysis of hydrocarbons. Fluid produced bypyrolysis reactions may mix with other fluids in a formation. Themixture would be considered pyrolyzation fluid or pyrolyzation product.As used herein, “pyrolysis zone” refers to a volume of a formation (forexample, a relatively permeable formation such as a tar sands formation)that is reacted or reacting to form a pyrolyzation fluid.

Unless specified otherwise, when a first quantity QUANT₁ ‘significantlyexceeds’ a second quantity QUANT₂, a ratio between (i) the greater ofthe two quantities MAX(QUANT₁, QUANT₂) and (ii) the lesser of the twoquantities MIN(QUANT₁, QUANT₂) is at least 1.5. In some embodiments,this ratio is at least 1.7 or at least 1.9.

Unless specified otherwise, a ‘significant majority’ refers to at least75%. In some embodiments, the significant majority may be at least 80%or at least 85% or at least 90%.

“Superposition of heat” refers to providing heat from two or more heatsources to a selected section of a formation such that the temperatureof the formation at least at one location between the heat sources isinfluenced by the heat sources.

“Tar” is a viscous hydrocarbon that generally has a viscosity greaterthan about 10,000 centipoise at 15° C. The specific gravity of targenerally is greater than 1.000. Tar may have an API gravity less than10°.

A “tar sands formation” is a formation in which hydrocarbons arepredominantly present in the form of heavy hydrocarbons and/or tarentrained in a mineral grain framework or other host lithology (forexample, sand or carbonate). Examples of tar sands formations includeformations such as the Athabasca formation, the Grosmont formation, andthe Peace River formation, all three in Alberta, Canada; and the Faja aformation in the Orinoco belt in Venezuela.

“Thermally conductive fluid” includes fluid that has a higher thermalconductivity than air at standard temperature and pressure (STP) (0° and101.325 kPa).

“Thermal conductivity” is a property of a material that describes therate at which heat flows, in steady state, between two surfaces of thematerial for a given temperature difference between the two surfaces.

“Thickness” of a layer refers to the thickness of a cross section of thelayer, wherein the cross section is normal to a face of the layer.

A “U-shaped wellbore” refers to a wellbore that extends from a firstopening in the formation, through at least a portion of the formation,and out through a second opening in the formation. In this context, thewellbore may be only roughly in the shape of a “V” or “U”, with theunderstanding that the “legs” of the “U” do not need to be parallel toeach other, or perpendicular to the “bottom” of the “U” for the wellboreto be considered “U-shaped”.

“Upgrade” refers to increasing the quality of hydrocarbons. For example,upgrading heavy hydrocarbons may result in an increase in the APIgravity of the heavy hydrocarbons.

“Visbreaking” refers to the untangling of molecules in fluid during heattreatment and/or to the breaking of large molecules into smallermolecules during heat treatment, which results in a reduction of theviscosity of the fluid.

“Viscosity” refers to kinematic viscosity at 40° unless otherwisespecified. Viscosity is as determined by ASTM Method D445.

“VGO” or “vacuum gas oil” refers to hydrocarbons with a boiling rangedistribution between 343° and 538° at 0.101 MPa. VGO content isdetermined by ASTM Method D5307.

The term “wellbore” refers to a hole in a formation made by drilling orinsertion of a conduit into the formation. A wellbore may have asubstantially circular cross section, or another cross-sectional shape.As used herein, the terms “well” and “opening,” when referring to anopening in the formation may be used interchangeably with the term“wellbore.”

A formation may be treated in various ways to produce many differentproducts. Different stages or processes may be used to treat theformation during an in situ heat treatment process. In some embodiments,one or more sections of the formation are solution mined to removesoluble minerals from the sections. Solution mining minerals may beperformed before, during, and/or after the in situ heat treatmentprocess. In some embodiments, the average temperature of one or moresections being solution mined may be maintained below about 120° C.

In some embodiments, one or more sections of the formation are heated toremove water from the sections and/or to remove methane and othervolatile hydrocarbons from the sections. In some embodiments, theaverage temperature may be raised from ambient temperature totemperatures below about 220° during removal of water and volatilehydrocarbons.

In some embodiments, one or more sections of the formation are heated totemperatures that allow for movement and/or visbreaking of hydrocarbonsin the formation. In some embodiments, the average temperature of one ormore sections of the formation are raised to mobilization temperaturesof hydrocarbons in the sections (for example, to temperatures rangingfrom 100° to 250°, from 120° to 240°, or from 150° to 230°).

In some embodiments, one or more sections are heated to temperaturesthat allow for pyrolysis reactions in the formation. In someembodiments, the average temperature of one or more sections of theformation may be raised to pyrolysis temperatures of hydrocarbons in thesections (for example, temperatures ranging from 230° to 900°, from 240°to 400° or from 250° to 350°).

Heating the hydrocarbon-containing formation with a plurality of heatsources may establish thermal gradients around the heat sources thatraise the temperature of hydrocarbons in the formation to desiredtemperatures at desired heating rates. The rate of temperature increasethrough mobilization temperature range and/or pyrolysis temperaturerange for desired products may affect the quality and quantity of theformation fluids produced from the hydrocarbon-containing formation.Slowly raising the temperature of the formation through the mobilizationtemperature range and/or pyrolysis temperature range may allow for theproduction of high quality, high API gravity hydrocarbons from theformation. Slowly raising the temperature of the formation through themobilization temperature range and/or pyrolysis temperature range mayallow for the removal of a large amount of the hydrocarbons present inthe formation as hydrocarbon product.

In some in situ heat treatment embodiments, a portion of the formationis heated to a desired temperature instead of slowly heating thetemperature through a temperature range. In some embodiments, thedesired temperature is 300°, 325°, or 350° Other temperatures may beselected as the desired temperature.

Superposition of heat from heat sources allows the desired temperatureto be relatively quickly and efficiently established in the formation.Energy input into the formation from the heat sources may be adjusted tomaintain the temperature in the formation substantially at a desiredtemperature.

Mobilization and/or pyrolysis products may be produced from theformation through production wells. In some embodiments, the averagetemperature of one or more sections is raised to mobilizationtemperatures and hydrocarbons are produced from the production wells.The average temperature of one or more of the sections may be raised topyrolysis temperatures after production due to mobilization decreasesbelow a selected value. In some embodiments, the average temperature ofone or more sections may be raised to pyrolysis temperatures withoutsignificant production before reaching pyrolysis temperatures. Formationfluids including pyrolysis products may be produced through theproduction wells.

In some embodiments, the average temperature of one or more sections maybe raised to temperatures sufficient to allow synthesis gas productionafter mobilization and/or pyrolysis. In some embodiments, hydrocarbonsmay be raised to temperatures sufficient to allow synthesis gasproduction without significant production before reaching thetemperatures sufficient to allow synthesis gas production. For example,synthesis gas may be produced in a temperature range from about 400° toabout 1200°, about 500° to about 1100°, or about 550° to about 1000° Asynthesis gas generating fluid (for example, steam and/or water) may beintroduced into the sections to generate synthesis gas. Synthesis gasmay be produced from production wells.

Solution mining, removal of volatile hydrocarbons and water, mobilizinghydrocarbons, pyrolyzing hydrocarbons, generating synthesis gas, and/orother processes may be performed during the in situ heat treatmentprocess. In some embodiments, some processes may be performed after thein situ heat treatment process. Such processes may include, but are notlimited to, recovering heat from treated sections, storing fluids (forexample, water and/or hydrocarbons) in previously treated sections,and/or sequestering carbon dioxide in previously treated sections.

FIG. 1 depicts a schematic view of an embodiment of a portion of the insitu heat treatment system for treating the hydrocarbon-containingformation. The in situ heat treatment system may include barrier wells1200. Barrier wells are used to form a barrier around a treatment area.The barrier inhibits fluid flow into and/or out of the treatment area.Barrier wells include, but are not limited to, dewatering wells, vacuumwells, capture wells, injection wells, grout wells, freeze wells, orcombinations thereof. In some embodiments, barrier wells 1200 aredewatering wells. Dewatering wells may remove liquid water and/orinhibit liquid water from entering a portion of the formation to beheated, or to the formation being heated. In the embodiment depicted inFIG. 1, the barrier wells 1200 are shown extending only along one sideof heater sources 1202, but the barrier wells typically encircle allheat sources 1202 used, or to be used, to heat a treatment area of theformation.

Heat sources 1202 are placed in at least a portion of the formation.Heat sources 1202 may include heaters such as insulated conductors,conductor-in-conduit heaters, surface burners, flameless distributedcombustors, and/or natural distributed combustors. Heat sources 1202 mayalso include other types of heaters. Heat sources 1202 provide heat toat least a portion of the formation to heat hydrocarbons in theformation. Energy may be supplied to heat sources 1202 through supplylines 1204. Supply lines 1204 may be structurally different depending onthe type of heat source or heat sources used to heat the formation.Supply lines 1204 for heat sources may transmit electricity for electricheaters, may transport fuel for combustors, or may transport heatexchange fluid that is circulated in the formation. In some embodiments,electricity for an in situ heat treatment process may be provided by anuclear power plant or nuclear power plants. The use of nuclear powermay allow for reduction or elimination of carbon dioxide emissions fromthe in situ heat treatment process.

When the formation is heated, the heat input into the formation maycause expansion of the formation and geomechanical motion. The heatsources may be turned on before, at the same time, or during adewatering process. Computer simulations may model formation response toheating. The computer simulations may be used to develop a pattern andtime sequence for activating heat sources in the formation so thatgeomechanical motion of the formation does not adversely affect thefunctionality of heat sources, production wells, and other equipment inthe formation.

Heating the formation may cause an increase in permeability and/orporosity of the formation. Increases in permeability and/or porosity mayresult from a reduction of mass in the formation due to vaporization andremoval of water, removal of hydrocarbons, and/or creation of fractures.Fluid may flow more easily in the heated portion of the formationbecause of the increased permeability and/or porosity of the formation.Fluid in the heated portion of the formation may move a considerabledistance through the formation because of the increased permeabilityand/or porosity. The considerable distance may be over 1000 m dependingon various factors, such as permeability of the formation, properties ofthe fluid, temperature of the formation, and pressure gradient allowingmovement of the fluid. The ability of fluid to travel considerabledistance in the formation allows production wells 1206 to be spacedrelatively far apart in the formation.

Production wells 1206 are used to remove formation fluid from theformation. In some embodiments, production well 1206 includes a heatsource. The heat source in the production well may heat one or moreportions of the formation at or near the production well. In some insitu heat treatment process embodiments, the amount of heat supplied tothe formation from the production well per meter of the production wellis less than the amount of heat applied to the formation from a heatsource that heats the formation per meter of the heat source. Heatapplied to the formation from the production well may increase formationpermeability adjacent to the production well by vaporizing and removingliquid phase fluid adjacent to the production well and/or by increasingthe permeability of the formation adjacent to the production well byformation of macro and/or micro fractures.

More than one heat source may be positioned in the production well. Aheat source in a lower portion of the production well may be turned offwhen superposition of heat from adjacent heat sources heats theformation sufficiently to counteract benefits provided by heating theformation with the production well. In some embodiments, the heat sourcein an upper portion of the production well may remain on after the heatsource in the lower portion of the production well is deactivated. Theheat source in the upper portion of the well may inhibit condensationand reflux of formation fluid.

In some embodiments, the heat source in production well 1206 allows forvapor phase removal of formation fluids from the formation. Providingheating at or through the production well may: (1) inhibit condensationand/or refluxing of production fluid when such production fluid ismoving in the production well proximate the overburden, (2) increaseheat input into the formation, (3) increase production rate from theproduction well as compared to a production well without a heat source,(4) inhibit condensation of high carbon number compounds (C₆hydrocarbons and above) in the production well, and/or (5) increaseformation permeability at or proximate the production well.

Subsurface pressure in the formation may correspond to the fluidpressure generated in the formation. As temperatures in the heatedportion of the formation increase, the pressure in the heated portionmay increase as a result of thermal expansion of in situ fluids,increased fluid generation and vaporization of water. Controlling rateof fluid removal from the formation may allow for control of pressure inthe formation. Pressure in the formation may be determined at a numberof different locations, such as near or at production wells, near or atheat sources, or at monitor wells.

In some hydrocarbon-containing formations, production of hydrocarbonsfrom the formation is inhibited until at least some hydrocarbons in theformation have been mobilized and/or pyrolyzed. Formation fluid may beproduced from the formation when the formation fluid is of a selectedquality. In some embodiments, the selected quality includes an APIgravity of at least about 20°, 30°, or 40°. Inhibiting production untilat least some hydrocarbons are mobilized and/or pyrolyzed may increaseconversion of heavy hydrocarbons to light hydrocarbons. Inhibitinginitial production may minimize the production of heavy hydrocarbonsfrom the formation. Production of substantial amounts of heavyhydrocarbons may require expensive equipment and/or reduce the life ofproduction equipment.

In some hydrocarbon-containing formations, hydrocarbons in the formationmay be heated to mobilization and/or pyrolysis temperatures beforesubstantial permeability has been generated in the heated portion of theformation. An initial lack of permeability may inhibit the transport ofgenerated fluids to production wells 1206. During initial heating, fluidpressure in the formation may increase proximate heat sources 1202. Theincreased fluid pressure may be released, monitored, altered, and/orcontrolled through one or more heat sources 1202. For example, selectedheat sources 1202 or separate pressure relief wells may include pressurerelief valves that allow for removal of some fluid from the formation.

In some embodiments, pressure generated by expansion of mobilizedfluids, pyrolysis fluids or other fluids generated in the formation maybe allowed to increase although an open path to production wells 1206 orany other pressure sink may not yet exist in the formation. The fluidpressure may be allowed to increase towards a lithostatic pressure.Fractures in the hydrocarbon-containing formation may form when thefluid approaches the lithostatic pressure. For example, fractures mayform from heat sources 1202 to production wells 1206 in the heatedportion of the formation. The generation of fractures in the heatedportion may relieve some of the pressure in the portion. Pressure in theformation may have to be maintained below a selected pressure to inhibitunwanted production, fracturing of the overburden or underburden, and/orcoking of hydrocarbons in the formation.

After mobilization and/or pyrolysis temperatures are reached andproduction from the formation is allowed, pressure in the formation maybe varied to alter and/or control a composition of formation fluidproduced, to control a percentage of condensable fluid as compared tonon-condensable fluid in the formation fluid, and/or to control an APIgravity of formation fluid being produced. For example, decreasingpressure may result in production of a larger condensable fluidcomponent. The condensable fluid component may contain a largerpercentage of olefins.

In some in situ heat treatment process embodiments, pressure in theformation may be maintained high enough to promote production offormation fluid with an API gravity of greater than 20°. Maintainingincreased pressure in the formation may inhibit formation subsidenceduring in situ heat treatment. Maintaining increased pressure may reduceor eliminate the need to compress formation fluids at the surface totransport the fluids in collection conduits to treatment facilities.

Maintaining increased pressure in a heated portion of the formation maysurprisingly allow for production of large quantities of hydrocarbons ofincreased quality and of relatively low molecular weight. Pressure maybe maintained so that formation fluid produced has a minimal amount ofcompounds above a selected carbon number. The selected carbon number maybe at most 25, at most 20, at most 12, or at most 8. Some high carbonnumber compounds may be entrained in vapor in the formation and may beremoved from the formation with the vapor. Maintaining increasedpressure in the formation may inhibit entrainment of high carbon numbercompounds and/or multi-ring hydrocarbon compounds in the vapor. Highcarbon number compounds and/or multi-ring hydrocarbon compounds mayremain in a liquid phase in the formation for significant time periods.The significant time periods may provide sufficient time for thecompounds to pyrolyze to form lower carbon number compounds.

Generation of relatively low molecular weight hydrocarbons is believedto be due, in part, to autogenous generation and reaction of hydrogen ina portion of the hydrocarbon-containing formation. For example,maintaining an increased pressure may force hydrogen generated duringpyrolysis into the liquid phase within the formation. Heating theportion to a temperature in a pyrolysis temperature range may pyrolyzehydrocarbons in the formation to generate liquid phase pyrolyzationfluids. The generated liquid phase pyrolyzation fluids components mayinclude double bonds and/or radicals. Hydrogen (H₂) in the liquid phasemay reduce double bonds of the generated pyrolyzation fluids, therebyreducing a potential for polymerization or formation of long chaincompounds from the generated pyrolyzation fluids. In addition, H₂ mayalso neutralize radicals in the generated pyrolyzation fluids. H₂ in theliquid phase may inhibit the generated pyrolyzation fluids from reactingwith each other and/or with other compounds in the formation.

Formation fluid produced from production wells 1206 may be transportedthrough collection piping 1208 to treatment facilities 1210. Formationfluids may also be produced from heat sources 1202. For example, fluidmay be produced from heat sources 1202 to control pressure in theformation adjacent to the heat sources. Fluid produced from heat sources1202 may be transported through tubing or piping to collection piping1208 or the produced fluid may be transported through tubing or pipingdirectly to treatment facilities 1210. Treatment facilities 1210 mayinclude separation units, reaction units, upgrading units, fuel cells,turbines, storage vessels, and/or other systems and units for processingproduced formation fluids. The treatment facilities may formtransportation fuel from at least a portion of the hydrocarbons producedfrom the formation. In some embodiments, the transportation fuel may bejet fuel, such as JP-8.

Formation fluid may be hot when produced from the formation through theproduction wells. Hot formation fluid may be produced during solutionmining processes and/or during in situ heat treatment processes. In someembodiments, electricity may be generated using the heat of the fluidproduced from the formation. Also, heat recovered from the formationafter the in situ process may be used to generate electricity. Thegenerated electricity may be used to supply power to the in situ heattreatment process. For example, the electricity may be used to powerheaters, or to power a refrigeration system for forming or maintaining alow temperature barrier. Electricity may be generated using a Kalinacycle, Rankine cycle or other thermodynamic cycle. In some embodiments,the working fluid for the cycle used to generate electricity is aquaammonia.

FIGS. 2A-2E illustrate a pattern of heaters 220 within a cross section(e.g. a horizontal or vertical or slanted cross section) of ahydrocarbon-bearing subsurface formation such as oil shale, tar sands,coals, bitumen-containing carbonates, gibsonite, or heavy oil-containingdiatomite). In some embodiments, each of the heaters (e.g. within heaterwells) includes an elongate section having an elongate/central axislocally perpendicular to the cross section of the subsurface formation.Each dot 220 in FIGS. 2A-2D represents a location of a cross section ofthe respective elongate heater in the plane defined by the subsurfacecross section. The heater spatial pattern of FIGS. 2A-2D, or the heaterpattern of any other embodiment, may occur at any depth within thesubsurface formation, for example, at least 50 meters or at least 100meters or at least 150 meters or at least 250 meters beneath thesurface, or more.

In the example of FIGS. 2A-2E, heaters 220 are respectively disposed atrelatively high and low spatial densities (and relatively short and longheater spacings) within nested inner 210 and outer 214 zones of thecross section of the hydrocarbon-bearing formation. In the particularexample of FIGS. 2A-2D, (i) nineteen inner zone heaters 226 are disposedat a relatively high density (and relatively short spacings betweenneighboring heaters) both within an inner zone 210 and around aperimeter 204 of the inner zone 210 (i.e. referred to as an ‘innerperimeter’), and (ii) twelve outer zone 228 heaters are arranged arelatively low density (and relatively long spacings between neighboringheaters) in outer zone 214 so as to be distributed around a perimeter208 of outer zone 214. In the non-limiting example of FIG. 2A-2E, withinouter zone 214, (i) all outer zone heaters are distributed around theperimeter 208 of outer zone 214, and (ii) the region between the inner204 and outer 208 perimeters is relatively free of heaters.

Because heater patterns are defined within a two-dimensionalcross-section of the subsurface formation, the terms ‘inner zone’ 210and ‘outer zone’ 214 refer to portions of the two-dimensional crosssection of the subsurface formation. Because heater patterns are definedwithin a two-dimensional cross-section of the subsurface formation,various spatial properties related to heater location such as heaterspacing, density, and ‘distance to heater’ are also defined within atwo-dimensional planar cross-section of the formation.

For the present disclosure, the ‘inner zone’ 210 refers to the entirearea enclosed by a perimeter 204 thereof. The ‘outer zone’ 214 refers tothe entire area, (i) outside of inner zone 210 that is (ii) enclosed bya perimeter 208 outer zone 214.

As will be discussed below, in some embodiments, the heater patternsillustrated in the non-limiting example of FIGS. 2A-2E, and in otherembodiments disclosed herein, are useful for minimizing and/orsubstantially minimizing a number of heaters 220 required to rapidlyreach a relatively-sustained substantially steady-state production rateof hydrocarbon fluids in the subsurface formation.

In some embodiments, during an initial phase of heater operation, thesubsurface formation within the smaller inner zone 210 heats uprelatively quickly, due to the high spatial density and short spacing ofheaters therein. This high heater spatial density may expediteproduction of hydrocarbons within inner zone 210 during an earlier phaseof production when the average temperature in the inner zone 210 exceeds(e.g. significantly exceeds) that of the outer zone 214. During a laterphase of operation, the combination of (i) heat provided by outer zoneheaters; and (ii) outward flow of thermal energy from inner zone 210 toouter zone 214 may heat the outer zone 214.

As will be discussed below (see, for example, FIGS. 4-7), in someembodiments two distinct ‘production peaks’ may be observed—an earlierinner zone production peak 310 and a later outer zone production peak330. In some embodiments, these production peaks collectively contributeto an ‘overall’ hydrocarbon production rate within the ‘combined’ region(i.e. the combination of inner 210 and outer 214 regions) that (i) rampsup relatively quickly due to the inner zone peak (i.e. has a ‘fast risetime’) and (ii) is sustained at a near-steady rate for an extendedperiod of time.

For the present disclosure, ‘inner zone perimeter 204’ or ‘innerperimeter 204’ which forms a boundary between inner 210 and outer 214zones, is considered part of inner zone 210. In the example of FIGS.2A-2E the twelve heaters located on the ‘inner hexagon’ 204 are innerzone heaters 226. The ‘outer zone perimeter 208’ or ‘outer perimeter208’ which forms a boundary between the outer zone 214 and ‘externallocations’ outside of the outer zone is considered part of outer zone214. The terms ‘inner zone perimeter 204’ and ‘inner perimeter 204’ areused interchangeably and have the same meaning; the terms ‘outer zoneperimeter 208’ and ‘outer perimeter 208’ are used interchangeably andhave the same meaning.

As illustrated in FIG. 2B, inner 210 and outer 214 zones are (i) nestedso that outer zone 214 surrounds inner zone 210, (ii) share a commoncentroid location 298, and (iii) have like-shaped perimeters 204, 208.In the example of FIGS. 2A-2E, inner 204 and outer 208 zone perimetersare both regular hexagons. In the non-limiting example of FIGS. 2A-2E,inner zone heaters are 226 dispersed throughout the inner zone atexactly a uniform spacing s. In the example if FIGS. 2A-2E, inner zoneheaters 226 are uniformly arranged on an equilateral triangular gridthroughout the inner zone 210—a length of each triangle side is s.

Within outer zone 214, an ‘average heater spacing’ is approximatelydouble that of the inner zone. Along outer perimeter 208, heaters aredistanced from each other by 2s. For every pair of adjacent heaterssituated on outer perimeter 208, a third heater on inner perimeter 206is distanced from both heaters of the pair of adjacent heaters by 2s.

In the example of FIGS. 2A-2E, twelve outer zone heaters are uniformlydistributed around regular hexagonally-shaped outer perimeter 208 sothat adjacent heaters on outer perimeter 208 (i) are separated by aseparation distance 2s; and (ii) subtend an angle equal to 30 degreesrelative to the center 298 of outer zone.

An area enclosed by inner perimeter 204 (i.e. an area of inner zone 210)is equal to 6√{square root over (3)}s² while an area enclosed by outerperimeter 208 (i.e. an area of the ‘combined area’ that is the sum ofinner 210 and outer 214 zones) is equal to 24√{square root over (3)}s²or four times the area enclosed by the inner perimeter 204. An arearatio between areas of the outer 210 and inner 214 zones is three.

The heater spatial density in inner zone 210 significantly exceeds thatwithin outer zone 214. As will be discussed below with reference to FIG.30, according to a ‘reservoir engineering’ definition of heater spatialdensity, the density within inner zone 210 of FIGS. 2A-2E is three timesthat of outer zone 214.

For the example of FIG. 2A-2E, the heater pattern includes a total of 31heaters. If the heaters were all drilled at the average inner zone 210spacing, a total of 61 heaters would be required. Compared to drillingall of the heaters at an average spacing within inner zone 210, thepattern of FIGS. 2A-2E requires only about half as many heaters.

In the example of FIGS. 2A-2E the inner zone and outer zone perimeters204, 208 are both regularly-hexagonally shaped. In some embodiments, theshapes of the inner and/or outer zone perimeters 204, 208 (andconsequently the shape of the inner 210 and/or outer 214 zones) aredefined by the locations of the heaters themselves—for example, theheater locations may define vertex locations for a polygon-shapedperimeter.

For example, in some embodiments, inner zone 210 may be defined by a‘cluster’ of heaters in a relatively high-spatial-density regionsurrounded by a region where the density of heaters is significantlylower. In these embodiments, the edge of this cluster of heaters wherean observable ‘density drop’ may define the border (i.e. inner zoneperimeter 204) between (i) the inner zone 210 where heaters are arrangedin a ‘cluster’ at a relatively high density and (ii) the outer zone 214.

In some embodiments, the perimeter of outer zone 208 may be defined by a‘ring’ (i.e. not necessarily circularly-shaped) of heaters outside ofinner zone 210 distributed around a centroid of outer zone 214. Thisring may be relatively ‘thin’ compared to the cluster of heaters thatform the inner zone 210. Overall, a local density within this ‘ring’ ofheaters defining outer zone perimeter 208 is relatively high compared tolocations adjacent to the ring—i.e. locations within outer zone 214(i.e. ‘internal locations’ within outer zone 214 away from inner-zone204 and outer-zone 208 perimeters) and outside of outer zone 214.

Alternatively or additionally, the inner and/or outer zone perimeters204, 208 are polygon shaped and are defined such that heaters (i.e. acentroid thereof in a cross-section of the subsurface where the heaterpattern is defined) are located at all polygon vertices of perimeters204, 208. As noted elsewhere, any heater pattern disclosed herein mayalso be a heater well pattern. As such, the perimeters 204, 208 may bedefined such that heater well centroids i.e. in a cross-section of thesubsurface where the heater pattern is defined) are located at allpolygon vertices of perimeters 204, 208.

Reference is now made to FIG. 2C. As illustrated in FIG. 2C, heaters arelabeled (i.e. for the non-limiting example of FIGS. 2A-2E) as inner zoneheaters 226 or outer zone heaters 228. In the example of FIGS. 2A-2E, 19heaters are inner zone heaters 226 and 12 heaters are outer zone heaters228. As illustrated in FIG. 2C, heaters may be labeled (i.e. for thenon-limiting example of FIGS. 2A-2D) as (i) ‘interior of inner zoneheaters’ 230 located in an ‘interior region’ of the inner zone 210 awayfrom the inner zone perimeter; (ii) inner perimeter heaters 232; (iii)interior of outer zone heaters' 234 located in an ‘interior region’ ofthe inner zone 210 away from the inner zone perimeter; and (iv) outerperimeter heaters 236. In the example of FIG. 2C, there are seven‘interior of inner zone heaters’ 230, twelve inner perimeter heaters232, zero interior of outer zone heaters' 234, and twelve outerperimeter heaters 236.

In the example of FIGS. 2A-2E and FIG. 3, inner 210 and outer 214 zonesare like-shaped and shaped as regular hexagons.

Some features disclosed herein may be defined relative to a‘characteristic length’ within inner 210 or outer 214 zones. For thepresent disclosure, a ‘characteristic length’ within a region of across-section of the subsurface formation is a square root of an area ofthe region. Thus, a ‘characteristic inner zone length’ is a square rootof an area of inner zone 210, and a ‘characteristic inner zone length’is a square root of an area of outer zone 214. For the ‘regular hexagon’example of FIGS. 2-3, (i) the area of inner zone 210 is 6√{square rootover (3)}s² so that the ‘characteristic inner zone length’ isapproximately 3.2s; (ii) an area of outer zone 214 is three times thatof inner zone 210 so that the ‘characteristic outer zone length’ isapproximately 5.6s.

It is appreciated that heaters are typically within heater wells (e.g.having elongate sections), any heater spatial pattern (and any featureor combination of feature(s)) disclosed herein may also be a heater wellpattern.

One salient feature of the pattern/arrangement of FIG. 2D is thepresence of production wells both within inner 210 and outer 214 zones.

In various embodiments, some or all (i.e. any combination of) thefollowing features related to ‘heater patterns’ may be observed:

(A) A heater spatial density, within the inner zone 210 significantlyexceeds that of the outer zone 214 and/or an ‘average spacing betweenneighboring heaters’ within the outer zone 214 significantly exceedsthat of the inner zone 210 and/or within outer zone 214, an averagedistance to a nearest heater significantly exceeds that of inner zone210. As will be discussed below with reference to FIGS. 4-7, in someembodiments, heater patterns providing this feature may be useful forexpediting a rate of conversion of kerogen and/or bitumen of thehydrocarbon-bearing formation into hydrocarbon fluids within inner zone210 so that an inner zone production peak 310 occurs in an earlier stageof production, and an outer zone production peak 330 only occurs after adelay.

(B) Inner zone heaters 226 and outer zone heaters 228 are distributed‘around’ respective centroids 298, 296 of inner 210 and outer 214 zones.As will be discussed below (see FIGS. 26A-26B), when heaters aredistributed ‘around’ a centroid then for every orientation of a‘reference ray’ starting at an ‘origin’ at the location of the centroid(296 or 298), at least one heater is located (i.e. the heater crosssection centroid is located) in every quadrant (i.e. every 90 degreesector) defined by the origin/centroid (296 or 298). In differentembodiments, heaters are arranged within inner 210 and/or outer 214zones so that inner zone heaters 226 or outer zone heaters 228 arepresent on every 72 degree sector or on every 60 degree sector or onevery 45 degree sector of inner or outer zones for every reference rayorientation.

(C) Outer zone heaters 228 are predominantly located on or near theouter zone perimeter 208. In some embodiments, the relatively highdensity of heaters in inner zone 210 causes an outward flow of thermalenergy from inner zone 210 into outer zone 214. Arrangement of outerzone heaters 228 so that they are predominantly located on or near theouter zone perimeter 208 may facilitate the ‘inward flow’ of thermalenergy so as to at least partly ‘balance’ the outward flow of thermalenergy into outer zone 214 from inner zone 210.

In some embodiments where heaters are deployed at most sparsely in theinterior portion of outer zone 210 away from inner and outer zoneperimeters 204, 208. This may be useful for reducing a number of heatersrequired to produce hydrocarbon fluids in a required manner.Furthermore, the relative lack of heaters within the ‘middle portion’ ofouter zone 210 (i.e. distanced from both perimeters 204, 208) may delayproduction of fluids from this middle portion of outer zone 210 andwithin outer zone 210 as a whole. As will be discussed below, withreference to FIGS. 4-7, this delay may be useful for producinghydrocarbon fluids in a manner where a significant production rate (e.g.at least half of a maximum production rate) is sustained for arelatively extended period of time.

(D) A ratio between areas enclosed by the outer 208 and inner 204perimeters is at least 3 or at least 3.5 and/or at most 10 or at most 9or at most 8 or at most 7 or at most 6 or at most 5 or at most 4.5and/or about 4. In the examples of FIGS. 2-4 and 7-9, this ratio isexactly four. In some embodiments, arranging heaters according to any ofthese ratios may be useful for producing hydrocarbons so that an overallrate of production ramps up relatively rapidly (i.e. short rise time)while is sustained for a relatively extended period of time. In someembodiment, if this ratio is too small, then the amount of time that therate of production is sustained may be too short and/or the thermalefficiency of the heater pattern may be reduced due to a reduction inthe re-use of thermal energy from inner zone heaters within outer zone210. If this ratio is too large, this may, for example, cause a dip inproduction after hydrocarbon fluids are rapidly produced within innerzone 210.

(E) The centroid 296 of inner zone 210 is located in a central portionof the region enclosed by outer zone perimeter 208—upon visualinspection of the heater patterns of FIGS. 2-11, it is clear that thisis true for all of these heater patterns. In some embodiments,substantially centering the inner zone within outer zone is useful forensuring that a higher fraction of thermal energy from heaters 226within inner zone 210 is re-used within outer zone 214, thus increasingthe overall thermal efficiency of the heater pattern. Unless specifiedotherwise, when centroid 296 of inner zone 210 is located in a centralportion of the region enclosed by outer zone perimeter 208, centroid 296of inner zone 210 is in the inner third of a region enclosed by outerzone perimeter 208. In some embodiments, centroid 296 of inner zone 210is in the inner quarter or inner fifth or inner sixth or inner tenth.

(F) In the example of FIGS. 2-11, there is no contact between perimeters204, 208 of inner 210 and outer zones 214. In some embodiments, at least30% or at least a majority of inner zone perimeter 204 is located awayfrom outer zone perimeter 214. In some embodiments, at least a majorityor at least a significant majority (i.e. at least 75%) of the inner zoneheaters are located away from the outer zone perimeter 208.

When an inner zone heater or a point on inner zone perimeter 204 islocated away from a perimeter 208 of outer zone 214, this means that thelocated away inner zone heater (or the located away point on inner zoneperimeter 204) is displaced from the outer zone perimeter 208 by atleast a threshold distance. Unless otherwise specified, this thresholddistance is at least one half of an inner zone average heater spacing.

Alternatively or additionally, in some embodiments, this thresholddistance is at least: (i) at least two-thirds of the inner zone averageheater spacing and/or (ii) at least the inner zone average heaterspacing or (iii) at least an average distance within inner zone (i.e.averaged over all locations within inner zone 210) to a nearest heater;and/or (ii) at least three times (or at least four times or at leastfive times) the square root of the area of the inner zone divided thenumber of inner zone heaters. In the example of FIGS. 2-3, the squareroot of the area of the inner zone is 3.2s and the number of inner zoneheaters is 19, so four times the square root of the area of the innerzone is about 0.51s. In the example of FIG. 4, the square root of thearea of the inner zone is 3.8s and the number of inner zone heaters is25, so four times the square root of the area of the inner zone is about0.44s.

(G) Perimeters 204, 208 of inner 210 and/or outer 214 zones are convexor substantially convex—the skilled artisan is directed to thedefinition of ‘substantially convex’ described below with reference toFIG. 29. In some embodiments, this may be useful for facilitatingoutward flow of heat generated by inner zone heaters located at or nearthe perimeter 204 of inner zone 210—e.g. so that heat from inner zoneheaters located at or near inner zone perimeter 204 flows outwards intoouter zone 214 and toward outer zone perimeter 208 rather than flowinginwards towards a centroid 296 of inner zone 210. In some embodiments,this increases the thermal efficiency of the heater pattern. In someembodiments, a candidate shape is ‘substantially convex’ if an areaenclosed by a minimally enclosed convex shape exceeds the area of thecandidate shape by at most 20% or at most 10% or at most 5%.

For the present disclosure, whenever something (i.e. an area or a closedcurve such as a perimeter of an area) is described as convex it may, insome embodiments be ‘substantially convex.’ Whenever something isdescribed as ‘substantially convex’ it may, in alternative embodimentsbe convex.

(H) An isoperimetric quotient of perimeters 204, 208 of the inner 210and/or outer 214 zone is at least 0.4 or at least about 0.5 or at least0.6. In the present disclosure, an ‘isoperimetric quotient’ of a closedcurve is defined as the isoperimetric coefficient of the area enclosedby the closed curve, i.e.

$\frac{4\pi \; A}{P^{2}}$

where P is the length of the perimeter of the closed curve, and A is thearea enclosed by the closed curve (e.g. an area of inner zone 210 forthe ‘closed curve’ defined by perimeter 204 or the sum of the areas ofinner 210 and outer 214 zones for the ‘closed curve’ defined byperimeter 208).

(I) An ‘aspect ratio’ of perimeter 204 of inner 210 and/or of perimeter208 of outer 214 zone is at most 5 or at most 4.5 or at most 4 or atmost 3.5 or at most 3 or at most 2.5 or at most 2.0 or at most 1.5. An“aspect ratio” of a shape (i.e. either the shape or an enclosingperimeter thereof) refers to a ratio between its longer dimension andits shorter dimension. In some embodiments, the inner and outer zoneshave a similar and/or relatively low aspect ratio that may be useful forefficient re-use of inner-zone-generated thermal energy within outerzone′ 214 and/or for obtaining a production curve exhibiting arelatively fast rise-time with sustained substantial production rate.

(J) Perimeters 204, 208 of inner 210 and/or outer 214 zones have commonshape characteristics. In some embodiments, inner and outer zoneperimeters 204, 208 are like-shaped. This is not a requirement. In someembodiments, IPQ_(INNER) is the isoperimeter quotient of inner zone 210,IPQ_(OUTER) is the isoperimeter quotient of outer zone 214,MAX(IPQ_(INNER), IPQ_(OUTER)) is the greater of IPQ_(INNER) andIPQ_(OUTER), MIN(IPQ_(INNER), IPQ_(OUTER)) is the lesser of IPQ_(INNER)and IPQ_(OUTER), and a ratio

$\frac{{MAX}\left( {{IPQ}_{INNER},{IPQ}_{OUTER}} \right)}{{MIN}\left( {{IPQ}_{INNER},{IPQ}_{OUTER}} \right)}$

is at most 3 or at most 2.5 or at most 2 or at most 1.75 or at most 1.5or at most 1.3 or at most 1.2 or at most 1.15 or at most 1.1 or at most1.05 or exactly 1.

(K) In some embodiments, heaters are ‘distributed substantiallyuniformly’ in inner 210 and/or outer 214 outer zone. This may allow formore efficient heating of inner zone 210. In some embodiments, visualinspection of a ‘heater layout’ diagram describing positions of heatercross sections is sufficient to indicate when heaters are ‘distributedsubstantially uniformly’ throughout one or more of the zone(s).

Alternatively or additionally, heaters may be distributed so as toprovide a relatively low ‘heater standard deviation spacing’ relative toa ‘heater average spacing in one or more of the zone(s).

Within any area of the subsurface formation (e.g. within inner zone 210or outer zone 214), there are a number of ‘neighboring heater spacings’within the area of the formation—for example, in FIG. 22C (i.e. thereare 36 spacings in outer zone 214 (i.e. 30 of the spacings have valuesof 2a and 6 of the spacings have values of √{square root over (3)}a) andthere are 32 spacings in inner zone 210 (i.e. all 36 of the spacingshave a value of a). In this example, the average spacing in inner zone210 is exactly a while the average spacing in outer zone 214 is

$\frac{{6\sqrt{3}a} + {30\left( {2a} \right)}}{36} \cong {1.95{a.}}$

It is also possible to compute a ‘standard deviation heater spacing’—inthe inner zone 214 this is exactly zero and in the outer zone the‘standard deviation heater spacing’ is

${\sqrt{\frac{{6\left( {{\sqrt{3}a} - {1.95a}} \right)^{2}} + {30\left( {{2a} - {1.95a}} \right)^{2}}}{36}} \cong \sqrt{\frac{{6\left( {0.048a^{2}} \right)} + {30\left( {0.0025a^{2}} \right)}}{36}} \cong \sqrt{\frac{0.363a^{2}}{36}}} = {0.1{a.}}$

In the example of FIG. 22C, a quotient of the standard deviation spacingand the average spacing is about 0.05.

In the example of FIGS. 5A and 24A, the average spacing is

$\frac{{17\sqrt{3}a} + {18a}}{35} \cong {1.87{a.}}$

In the example of FIGS. 5A and 25A, the ‘standard deviation heaterspacing’ is

${\sqrt{\frac{{17\left( {{\sqrt{3}a} - {1.87a}} \right)^{2}} + {18\left( {{2a} - {1.87a}} \right)^{2}}}{35}} \cong \sqrt{\frac{{17\left( {0.0196a^{2}} \right)} + {18\left( {0.0169a^{2}} \right)}}{36}} \cong {0.135a}},$

and a quotient of the standard deviation spacing and the average spacingis about 0.072.

In different embodiments, a quotient between a standard deviationspacing and an average spacing is at most 0.5 or at most 0.4 or at most0.3 or at most 0.2 or at most 0.1.

(L) In some embodiments, heaters are dispersed throughout inner zone 214rather than being limited to specific locations within inner zone (e.g.perimeter 204)—upon visual inspection of the heater patterns of FIGS.2-3, it is clear that this feature is true for all of these heaterpatterns. In some embodiments, the heaters are distributed according toan average heater spacing that is ‘small’ compared to some‘characteristic length’ of inner zone 210—for example, an average heaterspacing within inner zone 210 may be at most one-half or at mosttwo-fifths or at most one-third or at most one-quarter of the squareroot of an area of inner zone 210. This ‘close heater’ spacing relativeto a characteristic length of inner zone 210 may be useful for outwardlydirecting thermal energy from inner zone heaters so as to facilitateheat flow into outer zone 214.

In some embodiments, a ratio between (i) a product of a number of innerzone heaters 226 and a square of the average spacing in the inner zoneand (ii) an area of inner zone 210 is at least 0.75 or at least 1 or atleast 1.25 or at least 1.5.

In some embodiments, at least 10% or at least 20% or at least 30% or atleast 40% or at least 50% of inner zone heaters are ‘interior of innerzone heaters 230’ located within inner zone 210 away from inner zoneperimeter 204;

(M) One or more production wells located in inner 210 and/or outer 214zones. In some embodiments, one or more production wells (e.g. multipleproduction wells) are arranged within inner and/or outer zones toefficiently recovering hydrocarbon fluids from the subsurface. In someembodiments, locating production well(s) in inner zone 210 is useful forquickly removing hydrocarbon fluids located therein. In someembodiments, it is useful to locate production wells on different sidesof the inner zone so as to facilitate the fast and/or efficient removalof hydrocarbon fluids from the subsurface formation.

When two inner zone production wells having respective locationsLOC_(PROD) _(—) _(WELL) ^(IZ1) and LOC_(PROD) _(—) _(WELL) ^(IZ2) are‘are on different sides’ of inner zone 210 having centroid CENT_(IZ)298, the angle ∠LOC_(PROD) _(—) _(WELL) ^(IZ1)CENT_(IZ)LOC_(PROD) _(—)_(WELL) ^(IZ2) subtended by the locations of the two production wellsthrough inner zone centroid CENT_(IZ) 298 is at least 90 degrees (or atleast 100 degrees or at least 110 degrees or at least 120 degrees). Whenouter inner zone production wells having respective locations LOC_(PROD)_(—) _(WELL) ^(IZ1) and LOC_(PROD) _(—) _(WELL) ^(IZ2) are ‘are ondifferent sides’ of outer zone 214 having outer zone centroid CENT_(OZ)296, the angle ∠LOC_(PROD) _(—) _(WELL) ^(IZ1)CENT_(OZ)LOC_(PROD) _(—)_(WELL) ^(IZ2) subtended by the locations of the two production wellsthrough outer zone centroid CENT_(IZ) 298 is at least 90 degrees.

When two production wells having respective locations LOC_(PROD) _(—)_(WELL) ¹ and LOC_(PROD) _(—) _(WELL) ² are ‘are on different sides’ ofinner zone 210 having centroid CENT_(IZ) 298, the angle ∠LOC_(PROD) _(—)_(WELL) ¹CENT_(IZ)LOC_(PROD) _(—) _(WELL) ² subtended by the locationsof the two production wells through inner zone centroid CENT_(OZ) 296 isat least 90 degrees.

(N) A majority or a substantial majority of heaters within inner zone214 are distributed on a triangular or rectangular (e.g. square) orhexagonal pattern. In some embodiments, this allows for more efficientheating of inner zone 210;

For identical heaters spaced on a triangular heater well pattern, alloperating at constant power, the time t_(pyr) to heat the formation topyrolysis temperature by thermal conduction is approximately:

t _(pyr) ˜cD ² _(spacing) /D _(well)  (EQN. 1)

where D_(spacing) is the spacing between adjacent heater wells, D_(well)is the diameter of the heater wells, and c is a proportionality constantthat depends on the thermal conductivity and thermal diffusivity of theformation.

As noted above, heaters are deployed at a relatively high density withininner zone 210 and at a relatively low density within inner zone 214.Similarly, an ‘average spacing between neighboring heaters’ within theouter zone 214 significantly exceeds that of the inner zone 210.

In some embodiments, the amount of time required to pyrolyze kerogen(and/or to carry out any other in-situ hydrocarbon productionprocess—for example, producing hydrocarbon fluids from tar sands) issubstantially less in the inner zone 210 than in the outer zone due tothe relatively high heater density and/or relatively short heaterspacing in the inner zone 210.

FIGS. 4-7 present illustrative production functions describing a timedependence of the hydrocarbon production rate in a subsurfacehydrocarbon formation according to one illustrative example. It isexpected that a production function sharing one or more feature(s) withthat illustrated in FIGS. 4-7 may be observed when producinghydrocarbons using a two-level heater cell—for example, a two-levelheater cell having feature(s) similar that of FIG. 2D.

A number of illustrative hydrocarbon production functions related totwo-level heater cells are presented in FIGS. 4-7. In particular, thetime dependence of hydrocarbon fluid production rate in (i) the innerzone 210 (see inner zone production rate curve 354); (ii) outer zone 214(see outer zone production rate curve 358); (iii) the ‘combined’ regiondefined as the combination of inner 210 and outer 214 zones—this isequivalent to the area enclosed by a perimeter 208 of the outer zone(see combined region production rate curve 350), are all presented inaccordance with this illustrative example.

Because of the relatively ‘close’ heater spacing in the inner zone 210(i.e. in the example of FIG. 2D, the heater spacing in inner zone 210 isexactly one-half that of outer zone 214), temperatures in the inner zone210 rise more rapidly than in the outer zone 214, so as to expedite theproduction of hydrocarbons in the inner zone 210. In contrast, in mostlocations in the outer zone 214, a ‘hydrocarbon production temperature’(e.g. a pyrolysis temperature) is reached only after a significant timedelay.

In the example of FIG. 4, an inner zone production rate peak 310 occursbefore an outer zone production rate peak 330. During the interveningtime period, a production dip may be observed. In other examples, it maybe possible to minimize and/or eliminate the production dip—for example,by controlling (e.g. reducing) the power level of inner zone heaters 226relative to those 228 in outer zone 214.

Roughly speaking, the production rate peak occurs when a particular zoneor region reaches ‘hydrocarbon production temperature’—e.g. a pyrolysistemperature and/or a temperature where fluids are mobilized in a heavyoil formation and/or bitumen-rich formation and/or tar-sands formation.

As illustrated in FIG. 4, a production peak 330 of function 358describing production in outer zone 214 occurs after a production peak310 of function 354 describing production in inner zone 210. Thus, itmay be said that for a two-level heater cell having zones 210, 214(which may be written as {Zone₁,Zone₂} where Zone₁ is the innermost zone(or inner zone 210) and Zone₂ is the first zone outside of the innermostzone (or zone 214) that sequential production peaks {Peak₁,Peak₂}(labeled respectively as 310 and 330 in FIG. 4) are observedrespectively at times {t₁, t₂}. An amount of time required to ramp up tothe i^(th) peak Peak_(i) is t_(i).

For the example of FIG. 4, (i) the amount of time required to ramp up tothe production peak Peak₁ (labeled as 310 in FIG. 12) for the innermostzone Zone₁ (i.e. inner zone 210) is (t₁−t₀); and (ii) the amount of timerequired to ramp up to the production peak Peak₂ (labeled as 330 in FIG.4) for the zone Zone₂ (i.e. outer zone 214) immediately outside of theinnermost zone 210 is (t₂−t₀).

A peak time ramp-up time ratio between these two quantities is

$\frac{\left( {t_{2} - t_{0}} \right)}{\left( {t_{1} - t_{0}} \right)}.$

Inspection of FIG. 4 indicates that for the example FIG. 4, this ramp-uptime ratio is about three. In some embodiments, this peak time ramp-upratio is about equal to a zone area ratio between areas of the moreouter zone Zone₂ (i.e. outer zone 214) and the more inner zone Zone₁(i.e. inner zone 210). For the example of FIG. 2D, a ‘zone area ratio’between (i) an area of the more outer zone Zone₂ (i.e. outer zone 214);and (ii) an area of the more inner zone Zone₁ (i.e. inner zone 210) isthree. Thus, in some embodiments, for a more inner zone Zone₁ (e.g.inner zone 210) and a more outer zone Zone₂ (i.e. outer zone 214), a‘zone area ratio’ thereof is substantially equal to a ‘ramp-up time’ratio for times of their production Peak₁ peaks and Peak₂. In someembodiments, this is true at least in part because a reciprocal of a‘density ratio’ between heater densities in the more outer (i.e. outerzone 214) and the more inner zone (i.e. outer zone 214) is also equal tothe ramp-up is also equal to about three.

Also illustrated in FIGS. 4 and 7 is the overall or total rate ofhydrocarbon fluid in the ‘combined region’ (i.e. the area enclosedwithin outer zone perimeter 208—this is the combination of inner 210 andouter 214 zones), described by curve 350 having a production rate peak320 which occurs immediately before that 330 of outer zone 2140.

Inspection of combined region hydrocarbon fluid production rate curve350 indicates that: (i) similar to inner zone production curve 354,combined region production curve 350 ramps up relatively quicklyindicating a fast rise time; (ii) a ‘significant’ hydrocarbon productionrate (e.g. at least one-half of the maximum production rate) issustained for a relatively long period of time. In the example of FIGS.4 and 7, a ratio SPT/RT between a (i) a sustained production time SPT(i.e. the amount of time that the production rate is contiuouslysustained above one-half of a maximum production rate level for thecombined region) and (ii) a rise time RT for the combined region isrelatively ‘large’—e.g. at least four-thirds or at least three-halves orat least two.

For the present disclosure, a ‘half-maximum hydrocarbon fluid productionrate rise time’ or ‘half-maximum rise time’ is the amount of timerequired for hydrocarbon fluid production to reach one-half of itsmaximum, while the ‘half-maximum hydrocarbon fluid production ratesustained production time’ or the ‘half-maximum sustained productiontime’ is the amount of time where the hydrocarbon fluid production rateis sustained at least one-half of its maximum. FIGS. 5, 6 and 7respectively show production rate curves 354, 358 and 350 for the inner210, outer 214 and ‘total’ zones (i.e. the combination of inner andouter zones).

In FIGS. 4-7, a production dip (e.g. occurring after peak 310 and beforepeak 330) is illustrated.—In some embodiments, such a production dip (orany other production dip) may be observed even within a time period of a‘half-maximum hydrocarbon fluid production rate sustained productiontime’ as long as the production rate remains above one-half of a maximumrate throughout the time period of the ‘half-maximum hydrocarbon fluidproduction rate sustained production time’.

A relatively large SPT/RT ratio may describe situations where, (i)hydrocarbon fluids are produced (e.g. from kerogen or from bitumen) andremoved from the subsurface after only a minimal delay, allowing arelatively rapid ‘return’ on investment in the projection while usingsubstantially only a minimal number of heaters; and (ii) hydrocarbonfluids are produced for a relatively extended period of time at arelatively constant rate. Because hydrocarbon fluids are produced at arelatively constant rate, a ratio between a peak hydrocarbon productionrate and an average hydrocarbon production rate for the combined region,is relatively small. In some embodiments, the amount of infrastructurerequired for hydrocarbon fluid production and/or processing isdetermined at least in part by the maximum production rate. In someembodiments, a relatively low ratio between a peak hydrocarbonproduction rate and an average hydrocarbon production rate for thecombined region may reduce the amount of infrastructure required forfluid production and/or processing with a minimal number, or nearminimal number, of pre-drilled heater wells.

It is appreciated that none of the examples relating to illustrativeproduction functions are limiting. It may be possible to change theshape of this function, for example, by operating heaters at differentpower levels.

Also illustrated in FIG. 14A are the earlier 980 and later 984 stages ofproduction. During the earlier 980 stage of production, hydrocarbonfluids are produced primarily in inner 210 zone; during the later 984stage of production, hydrocarbon fluids are produced primarily in outer214 zone.

FIG. 12E is a flowchart of a method for producing hydrocarbon fluids. Instep S1551, wells are drilled into the subsurface formation. In stepS1555, heaters are installed in the heater wells—it is appreciated thatsome heaters may be installed before all heater wells or productionwells are drilled.

In step S1559, the pre-drilled heaters are operated to producehydrocarbon fluids such that a ratio between a half-maximum sustainedproduction time and a rise time is at least four-thirds, or at leastthree-halves, or at least seven quarters or at least two. In someembodiments, this is accomplished using any inner zone and outer zoneheater pattern disclosed herein. In some embodiments, at least amajority of the outer zone heaters commence operation when at most aminority of inner zone hydrocarbon fluids have been produced.

In some embodiments, any heater pattern disclosed herein (e.g. relatingto two-level heater cells) may be thermally efficient. In particular, insome embodiments, at least 5% or at least 10% or at least 20% of thethermal energy used for outer zone hydrocarbon fluid production issupplied by outward migration (e.g. by heat conduction and/orconvection) of thermal energy from the inner zone 210 to the outer zone214.

Once the production rate in the inner zone has dropped by a certainthreshold (for example, by at least 30% or at least 50% and/or at most90% or at most 70% of a maximum production rate), this may indicate thata hydrocarbon fluid production temperature (e.g. a temperature whichresults in mobilized fluids, visbreaking, and/or pyrolysis ofhydrocarbon-containing material so that mobilized fluids, visbrokenfluids, and/or pyrolyzation fluids are produced in the formation) hasbeen reached throughout most of the inner 210 zone—e.g. a pyrolysistemperature or a temperature for mobilizing hydrocarbon fluids), evenwhen significant portions of the outer 214 zone (e.g. at least 30% of ora majority of) are at a significantly cooler temperature. Studiesconducted by the present inventors indicated that once this inner-zoneproduction drop has occurred, the ability of the inner-zone heaters toexpedite fluid production is significantly reduced, and thus furtherfull-power operation of the inner-zone heaters may be of only marginalutility, and may not justify the energy ‘cost.’

In some embodiments, it is useful to shut off and/or reduce power to theinner zone heaters even while the outer zone heaters continue to operateat about the same power level.

As illustrated in FIG. 8, in some embodiments, the heater pattern ofFIG. 2A, or of any other embodiment disclosed herein (for example, seeany of FIGS. 2-3) may repeat itself. Thus, in some embodiments, anyinner zone-outer zone heater pattern disclosed herein may be a ‘unitcell’ heater pattern which repeats itself. Since any heater patterndisclosed herein (and any feature(s) thereof or combination thereof) mayalso be a ‘heater well pattern,’ the heater well pattern of FIG. 2A, orof any other embodiment disclosed herein, may repeat itself.

In the example of FIG. 8, the heater pattern of FIG. 2A exactly repeatsitself in each cell so as to fill space of a subsurface formation—i.e.the unit heater cells are identical. As illustrated in the example ofFIGS. 11-12, the ‘identical cell’ feature is not a limitation and heatercells are not required to be exactly repeating unit cells. In someembodiments, each heater cell may individually provide common features(i.e. any combination of features disclosed herein including but notlimited to features related to heater spacing features, heater spatialdensity feature(s), features related to size(s) and/or shape of innerand/or outer zones (or relationships between them), production wellfeatures, features relating to operation of heaters or any otherfeature).

In the example of FIGS. 11-12, for each heater cell, an area enclosed byouter zone perimeter 208 is about four times that of inner zoneperimeter 204, a heater density within inner zone 210 significantlyexceeds that of outer zone 214, at least a substantial majority of theinner zone heaters 226 are located away from outer zone perimeter 208,production well(s) are located in each of inner 210 and outer 214 zones.

In the example of FIGS. 8-12, for a plurality of the heater cells, (i)the area of all cells are substantially equal to a single common value;(ii) for each heater cell of the plurality of cells, a significantportion (i.e. at least one third or at least one half or at leasttwo-thirds or at least three-quarters) of each cell perimeter (e.g.outer zone perimeter 208) is located ‘close’ to a neighboring cellperimeter.

A ‘candidate location’ of a first heater cell (i.e. within the cell oron a perimeter thereof—e.g. cell A 610) is located ‘close to’ a secondheater cell (e.g. cell B 614 or C 618) if a distance between (i) the‘candidate location’ of the first heater cell and (ii) a location of thesecond heater cell that is closest to the ‘candidate location’ of thefirst heater cell is less than a ‘threshold distance.’ Unless otherwisespecified, this ‘threshold distance’ is at most two-fifths of a squareroot of an area of the first heater cell. In some embodiments, this‘threshold distance’ is at most one third or at most one quarter or atmost one sixth or at most one tenth of a square root of an area of thefirst heater cell.

In some embodiments, for each of first and second neighboring heatercells (e.g. having substantially equal areas), at least a portion (e.g.at least 5% or at least 10% or at least 20% or at least 30% or at least40% or at least a majority of) of each cell perimeter selected from oneof the first and second heater cells) is ‘close’ to the other heatercell.

In the example of FIG. 8, one of the cells is a ‘surrounded cell’whereby an entirety of its perimeter is ‘close to’ neighboring heatercells. For the present disclosure, a heater cell is ‘substantiallysurrounded’ when a substantial majority (i.e. at least 75%) of itsperimeter is ‘close to’ a neighboring heater cell. In the example ofFIG. 8, different portions of a perimeter of surrounded cell 608 are‘close to’ six different neighboring heater cells. In some embodiments,different portions of a perimeter of surrounded cell 608 are ‘close to’at least 3 or at least 4 or at least 5 different neighboring cells—e.g.a majority of which or at least 3 or at least 4 or at least 5 of whichhave an area that is ‘substantially equal’ to that of surrounded cell608.

Also labeled in FIG. 8 are first 602 and second 604 neighboring cells,which are located on opposite sides of surrounded cell 608. In thepresent disclosure, two neighboring cells CELL¹ _(NEIGHBOR) and CELL²_(NEIGHBOR) having respective centroids ∠CENT(CELL₁ ^(NEIGHBOR)) andCENT(CELL² _(NEIGHBOR)) are said to be ‘substantially on opposite sites’of a candidate heater cell CELL_(CANDIDATE) having a centroidCENT(CELL_(CANDIDATE)) if an angle ∠CENT(CELL_(NEIGHBOR)¹)CENT(CELL_(CANDIDATE))CENT(CELL_(NEIGHBOR) ²) is at least 120 degrees.In some embodiments, this angle is at least 130 degrees or at least 140degrees or at least 150 degrees.

One salient feature of the multi-cell embodiment of FIG. 8-12 is thatneighboring cells may ‘share’ one or more (e.g. at least two) commonouter perimeter heaters 236. In this situation, each of the sharedheater serves as an outer perimeter heater for two or more neighboringcells. In the example of FIG. 8, neighboring heater cells may share upto three common outer perimeter heaters.

Without limitation, in some embodiments, the multi-cell pattern basedupon nested hexagons (e.g. having two levels as illustrated in FIG. 8 orhaving three or levels as discussed below) may provide one or more ofthe following benefits: (i) a significantly lower heater well density(e.g. at most three-thirds or at most three-fifths or at most one-half)compared to what would be observed for the hypothetical case where allheaters were arranged at a uniform density equal to that of the innerzones 210; (ii) a relatively short time to first production (e.g. seeFIG. 4-7); (iii) a lower energy use due to heat exchange between zonesand/or between neighboring cells; and/or (iv) due to the presence ofproduction wells in inner zones as well as outer zones, more oil andless gas is produced because fluids pas near fewer heater wells en routeto a production well—hence, less cracking.

It appreciated that other embodiments other than that of FIG. 8 mayprovide some or all of the aforementioned benefits.

The pattern of FIG. 9 is similar to that of FIG. 8—however, in theexample of FIG. 9 production wells are arranged at the centroid 296, 298of each heater cell, while in the example of FIG. 8 heaters are arrangedat the centroid 296, 298 of each heater cell.

In FIG. 10, a region of subsurface formation is filled with multipleheater cells including cell “A” 610, cell “B” 614 and cell “C” 618. Asillustrated in FIG. 10, cells “A” 610 and “C” 618 share common outerzone perimeter heater “W” 626; cells “A” 610 and “B” 614 share commonouter zone perimeter heater “X” 639; cells “B” 614 and “C” 618 sharecommon outer perimeter heater “Y” 638.

As illustrated in FIGS. 12-13, in some embodiments, the heater cells donot have identical patterns, and the heater cells may be thought of as‘quasi-unit cells’ rather than ‘unit cells.’ In the example of FIGS.12-13, even though heater cells are not identical, each heater cellindividually may contain any combination of feature(s) relating to inner210 and outer 214 zones described in any embodiment herein. The featuresinclude but are not limited to features related to heater spacing (e.g.shorter average spacing between neighboring heaters in inner zone 214than in outer zone 210), heater density (e.g. higher density in innerzone 214 than in outer zone 210), dimensions of inner and/or outer zoneperimeters 204, 208 (e.g. related to aspect ratio, or related to a ratiobetween respective areas of outer and inner zones or of areas enclosedby perimeters 204, 208 thereof), average distance to a nearest heater,dispersion and/or distribution of heaters within inner and/or outerzone, heater distribution along inner and/or outer zone perimeter(s)204, 208, or any other feature (e.g. including but not limited tofeature(s) related to heater location).

In the example of FIGS. 12-13, neighboring cells all have like-shapedand like-sized inner zone and outer zone perimeters 204, 208. This isnot a limitation. In some embodiments, areas or aspect ratios of innerzone and/or outer zone perimeters 204, 208 of neighboring cells (i.e.which optionally share at least one common outer zone heater) may besimilar but not identical. In some embodiments, for any ‘cell’ pairCELL₁, CELL₂ of neighboring heater cells CELL₁, CELL₂ an area enclosedby inner zone and/or outer zone perimeters 204, 208 of CELL₁ is (i)equal to at least 0.5 times and at most 2.0 times that of CELL₂ or (ii)equal to at least 0.666 times and at most 1.5 times that of CELL₂; or(iii) equal to at least 0.8 and at most 1.2 times that of CELL₂. In someembodiments, for any pair of neighboring heater cells CELL₁, CELL₂ anaspect ratio of inner zone and/or outer zone perimeters 204, 208 ofCELL₁ is (i) equal to at least 0.5 times and at most 2.0 times that ofCELL₂ or (ii) equal to at least 0.666 times and at most 1.5 times thatof CELL₂; or (iii) equal to at least 0.8 and at most 1.2 times that ofCELL₂.

In some embodiments, any feature(s) in the previous paragraph relatingany pair of neighboring heater cells CELL₁, CELL₂ may be true for atleast one pair of neighboring heater cells CELL₁, CELL₂. In someembodiments, any feature(s) may be true for various pair sets of cells.For example, if a cell CELL_(GIVEN) surrounded by a plurality ofneighbors CELL_(NEIGHBoR) _(—) ₁, CELL_(NEIGHBoR) _(—) ₂, . . .CELL_(NEIGHBOR) _(—) _(N), any feature(s) of the previous paragraphprevious paragraph may be true for at least a majority, or for all ofthe following cell pairs: {CELL_(GIVEN), CELL_(NEGHBoR) _(—) ₁},{CELL_(GIVEN), CELL_(NEIGHBOR) _(—) ₂}, . . . , {CELL_(GIVEN),CELL_(NEIGHBOR) _(—) _(N)}.

In some embodiments, a region of the subsurface formation (i.e. atwo-dimensional portion of a cross-section of the subsurface formation)may be ‘substantially filled’ by a plurality of heater cells if at least75% or at least 80% or at least 90% of the area of the region isoccupied by one of the heater cells. In some embodiments, the‘cell-filled-region’ includes at least 3 or at least 5 or at least 10 orat least 15 or at least 20 or at least 50 or at least 100 heater cellsand/or is rectangular in shape and/or circular in shape or having anyother shape and/or has an aspect ratio of at most 3 or at most 2.5 or atmost 2 or at most 1.5. In some embodiments, any feature(s) relatingpairs of neighboring cells (i.e. relating to the sharing of outerperimeter heaters 236 or related to neighboring pairs of heaters {CELL₁,CELL₂}) may be true for a majority of heater cells (or at least 75% ofthe heater cells or at least 90% of the heater cells) within thecell-filled region. In some embodiments, both a ‘length’ and a ‘width’of the cell-filled region (i.e. measured in heater cells) may be atleast 3 or at least 5 or at least 10 or at least 20 heater cells.

FIGS. 2-12 relate to heater patterns having at least two ‘levels’—i.e.an inner zone 210 having relatively high heater density and an outerzone 214 having relatively low heater density. In the examples of FIGS.13-14, one or more heater cells have at least ‘three’ levels.

OZS additional zone heaters (i.e. heaters located OZS additional zoneperimeter 202 or in an interior of OZS additional zone 218) include OZSadditional zone perimeter heaters each located on or near OZS additionalzone perimeter 202 and distributed around OZS additional zone perimeter202. In some embodiments, OZS additional zone heaters are predominantlyOZS additional zone perimeter heaters—this is analogous to the featureprovided by some embodiments and described above whereby outer zoneheaters 228 are predominantly outer zone perimeter heaters 236.

For the present disclosure, the OZS 210 refers to the entire areaenclosed by a perimeter 202 thereof. that is also outside of outer zone214.

In the example of FIG. 13, an area enclosed by a perimeter 202 of OZSadditional zone 218 and four times that of outer zone perimeter 202, andan average heater spacing within OZS additional zone 218 is about twicethat of outer zone 214. In the example of FIG. 13, perimeters 204, 208,202 of inner, outer and OZS-additional zones 210, 214, 218, areregular-hexagonal in shape and have respective side lengths equal to 2s,4s, and 8s. In the example of FIG. 13, respective average heaterspacings of inner 210, outer 214, and OZS additional 218 zones are equalto s, approximately equal to 2s, and approximately equal to 4s. Indifferent embodiments, a perimeter 202 of OZS additional zone 218 isconvex or substantially convex.

In different embodiments, a relation between OCS additional zone 218 andouter zone 214 is analogous to that between outer zone 214 and innerzone 210. Thus, in some embodiments, by analogy, any feature describedherein a relationship between inner 210 and outer 214 zones may also beprovided for outer 214 and OZS additional 218 zones. Such featuresinclude but are not limited to features related to heater spacing (e.g.shorter average spacing between neighboring heaters in inner zone 214than in outer zone 210), heater density (e.g. higher density in innerzone 214 than in outer zone 210), dimensions of inner and/or outer zoneperimeters 204, 208 (e.g. related to aspect ratio, or related to a ratiobetween respective areas of outer and inner zones or of areas enclosedby perimeters 204, 208 thereof), average distance to a nearest heater,dispersion and/or distribution of heaters within inner and/or outerzone, heater distribution along inner and/or outer zone perimeter(s)204, 208, or any other feature (e.g. including but not limited tofeature(s) related to heater location).

As was noted above for the case of a perimeter 208 of outer zone 214, indifferent embodiments the perimeter 202 of OZS additional zone 218 maybe defined by locations of the heater (i.e. to form some a ring-shapedcluster where adjacent locations have a significantly lower heaterdensity).

In the example of FIG. 13, production wells 224 are arranged througheach of inner 210, outer 214, and OZS additional zone 218, and arerespectively labeled in FIG. 13 as inner zone 2241, outer zone 2240 andadditional zone 224A production wells. In the example of FIG. 13, thedensity of production wells is greatest in the most inner zone (i.e.inner zone 210), is the least in the most outer zone (i.e. additionalzone 218) and has an intermediate value in the ‘mediating’ zone (i.e.outer zone 214). In particular, a ratio between an inner zone productionwell density and that of outer zone 210 is three; a ratio between anouter zone production well density and that of additional zone 214 isalso three.

In the particular example of FIG. 13, perimeters 208, 202 of outer 214and OZS-additional 218 zones are like shaped. As illustrated in FIGS.13-14, this is not a limitation.

Even though perimeters 208, 204 of outer 214 and inner 210 zones are notrequired to be like-shaped but they may share certainshape-properties—for example, an aspect ratio (see, for example FIGS.10A-10B) or any other shape-related parameter discussed herein.

Embodiments of the present invention relate to patterns of ‘heaters.’The heaters used may be electrical heaters, such as conductor-in-conduitor mineral-insulated heaters; downhole gas combustors; or heaters heatedby high temperature heat transfer fluids such as superheated steam,oils, CO₂, or molten salts or others. Because the outer zones 214 ofheaters may be energized for a substantially longer time than the innerzone of heaters, for example, four times or eight times longer (see FIG.13A), a heater with high reliability and long life is preferred for theouter 214 or OZS additional 218 zones. Molten salt heaters have verylong lifetimes because they operate at nearly constant temperaturewithout hot spots, and in many chemical plant and refinery applications,molten salt heaters have been operated for decades without shutdown. Inaddition, molten salt heaters may have very high energy efficiency,approaching 80%, and over the lifetime of the reservoir most of thethermal energy will be supplied to the oil shale from the heaters in thezones with the longest spacing.

FIG. 15A is an image of an exemplary electrical heater. FIG. 15B is animage of an exemplary molten salt heater. FIG. 15C is an image of anexemplary downhole combustion heater; FIG. 15D is a cross section of thedownhole portion of the the heater of FIG. 15C. For an additionaldiscussion of types of heaters and various features thereof, the skilledartisan is referred to U.S. Pat. No. 7,165,615, U.S. Pat. No. 6,079,499,U.S. Pat. No. 6,056,057 and US patent publication 2009/0200031, whichare all incorporated herein by reference in their entireties. In someembodiments, molten salt is continuously flowed through the heater. Forexample, hot molten salt (e.g. heated by a gas furnace) may becontinuously forced through the molten salt heater to replace thethermal energy lost by the molten salt within the heater to theformation.

A schematic of an advection-based heater is illustrated in FIG. 15E.Although the source of hot heat transfer fluid is illustrated in thefigures as above the surface, this is not a requirement—alternatively oradditionally, it is possible to heat the heat transfer fluid at one ormore subsurface location(s).

FIGS. 16A-16D relate to ‘heaters powered primarily by fuel combustion’.In the example of FIG. 16A, a fuel (e.g. a fossil fuel) is combusted,thermal energy of the fuel combustion generates steam which drives asteam turbine to produce electricity. The electrical heater (forexample, similar to FIG. 15A) is powered by the fuel-combustion-derivedelectricity. Examples of fuels which may be combusted include but arenot limited to methane, natural gas, propane, flue gas, coal andhydrogen gas. In the example of FIG. 16B, a gas turbine powered by gascombustion generates electricity supplied to the electrical heater.Other examples of “heaters powered primarily by fuel combustion” areillustrated in FIGS. 16C-16D (i.e. a particular case of the heater ofFIG. 15E) where the generated electricity (i.e. from the steam turbineor the gas turbine) is used to resistively heat a material (e.g. aferromagnetic material) in thermal contact with a heat transfer fluid(one example of a heat transfer fluid is a molten salt; another exampleis a synthetic oil; another example is molten metal). In the example ofFIGS. 16C-16D, the heat transfer fluid is heated above the surface wherethe resistively-heated material (i.e. which receives electrical currentderived from combustion of fossil fuel) is located within anabove-surface storage tank. This is not a limitation. Alternatively oradditionally, the heat transfer fluid may be heated in thesubsurface—e.g. the resistively-heated material through which electricalcurrent flow (i.e. electrical current derived from fuel combustion) maybe located in the subsurface. The examples of FIGS. 16A-216D relate tothe situation wherein thermal energy of combustion is used to generateelectricity. This is not a limitation. Other examples of ‘heaterspowered primarily by combustion’ are illustrated in FIGS. 15C-15Ddiscussed above.

In contrast to the heaters of FIGS. 15C-15D and 16A-16D which are‘heaters powered primarily by combustion,’ the heaters of FIGS. 17A-17Bare powered ‘primarily by electricity generated from wind.’ In theexample of FIG. 17A, electricity generated from wind is used toresistively heat a material (e.g. a ferromagnetic material) in thermalcommunication with a heat transfer fluid. In the example of FIG. 17A,the heat transfer fluid is heated above the surface where theresistively-heated material (i.e. which received electricity derivedfrom wind) is located in an above-surface fluid storage tank. This isnot a limitation. Alternatively or additionally, the heat transfer fluidmay be heated in the subsurface—e.g. the resistively-heated material(i.e. through which electrical current generated from wind) may belocated in the subsurface. In the example of FIG. 17B, an electricalheater is powered by electricity generated from wind.

Any electrical heater may include a voltage control system (NOT SHOWN).

In some embodiments, the turbine may be a microturbine—for example,available from the Capstone Turbine Corporation (United States).

Reference is now made to FIG. 18-19. In the inner zone, at least amajority or at least ⅔ of the heaters are powered primarily byelectricity from wind.

In contrast, in the outer zone a majority of at least ⅔ of the heatersare powered primarily by fuel combustion—hot fluids from the combustedfuel may be directly circulated within the subsurface (see FIGS.15C-15D) or thermal energy from the fuel combustion may be used togenerate electricity (see FIGS. 16A-16C).

Reference is now made to FIG. 20-21. In the inner zone, at least amajority or at least ⅔ of the heaters are powered primarily by fuelcombustion—hot fluids from the combusted fuel may be directly circulatedwithin the subsurface (see FIGS. 15C-15D) or thermal energy from thefuel combustion may be used to generate electricity (see FIGS. 16A-16C).

In contrast, in the outer zone at a majority or at least ⅔ of at least asubstantial majority of the heaters are powered primarily by electricitygenerated from wind.

Some embodiments relate to ‘neighboring heaters’ or ‘average spacingbetween neighboring heaters.’ Reference is made to FIGS. 22A-B. In FIG.22A, heaters are arranged according to the same heater pattern as inFIGS. 2A-2D, and heaters are labeled as follows: seven of the outerperimeters heaters are labeled 220A-220G, and nine of the inner zoneheaters are labeled as 220H-220P. FIG. 22B illustrates a portion of theheater pattern of FIG. 22A.

It is clear from FIG. 22A that some heaters may be said to ‘neighboreach other’ (for example, heaters 220C and 220D are ‘neighbors,’ heaters220C and 220J are ‘neighbors,’ heaters 220J and 220K are ‘neighbors’)while for other heaters, this is not true. Heaters 220C and 220L of the‘heater pair’ (220C,220L) are clearly not ‘neighbors.’ This is because‘heater-connecting-line segment’ Seg_Connect(220C,220L) connectingheaters (i.e. connecting the centroids of their respective crosssections) of the pair (220C,220L), having a length 2√{square root over(3)}s, crosses at least one shorter ‘heater-connecting-line segment,’ asillustrated in FIG. 22B. In particular, ‘heater-connecting-line segment’Seg_Connect(220C,220L) crosses (i) Seg_Connect(220D,220K) having alength of √{square root over (3)}s and (ii) Seg_Connect(220D,220J)having a length of 2s.

FIG. 22C illustrate the same heaters as in FIG. 22B—line segments of‘neighboring heater pairs’ are illustrated. In the example of FIG. 22C,the neighboring heater pairs are as follows: {Heater 220C, Heater 220D};{Heater 220D, Heater 220E}; {Heater 220E, Heater 220L}; {Heater 220K,Heater 220L}; {Heater 220J, Heater 220K}; {Heater 220C, Heater 220J};{Heater 220D, Heater 220J}; {Heater 220D, Heater 220K}; {Heater 220D,Heater 220L},

FIG. 23A illustrates the same heater pattern as that of FIGS. 2A-2D andFIG. 22A. In FIG. 22C, lines between neighboring heaters areillustrated. Within the outer zone 214, the average line length, or theaverage ‘heater spacing’ is around 1.95s, or slightly less than 2s.Within the inner zone 210, the average line length, or the average‘heater spacing’ is exactly s.

FIG. 23B illustrates ‘connecting line segments’ between neighboringheaters. Within the inner zone 210 of the example of FIG. 23B, theaverage line length, corresponding to the average heater spacing, isexactly s.

Two heaters Heater_(A), Heater_(B) are ‘neighboring heaters’ if theconnecting line segment between them (i.e. between their respectivecentroids) does not intersect a connecting line segment between twoother heaters Heater_(C), Heater_(D) in the subsurface formation. A‘heater-connecting-line-segment between neighboring heaters’ is‘resident within’ a region of the subsurface formation (i.e. atwo-dimensional cross-section thereof) if a majority of the length ofthe ‘heater-connecting-line-segment’ is located within the region of thesubsurface formation.

FIGS. 23C-24 respectively illustrate ‘connecting lines’ betweenneighboring heaters.

For the present disclosure, an ‘average spacing between neighboringheaters’ and an ‘average heater spacing’ are used synonymously.

Embodiments of the present invention relate to inner perimeter heaters232, outer perimeter heaters 236 and ‘OZS additional zone perimeterheaters.’ As discussed earlier, in some embodiments, the locations ofthe heaters determine the locations of the perimeters 204, 208 (and byanalogy 202) of inner 210, outer 214 or OZS additional 218 zones. Inthis case, inner perimeter heaters 232, outer perimeter heaters 236, andOSC-additional-zone perimeter heaters respectively are located onperimeters 204, 208, 202.

Alternatively, these perimeters 204, 208, 202 may be determined by apredetermined shape—e.g. a rectangle or regular hexagon or any othershape. For the latter case, there is no requirement for the innerperimeter heaters 232 to be located exactly on inner zone perimeter204—it is sufficient for the heater to be located near innerperimeter—e.g. in a ‘near-inner-perimeter’ location within inner zone210 or within outer zone 214. By analogy, the same feature is true forouter zone perimeter 208 or OZS-additional zone perimeter 202.

This is illustrated in FIGS. 25A-25B which illustrate: (i) locations inthe interior 610 of the inner zone 210; (ii) locations 614 in inner zone210 that are ‘substantially on’ inner zone perimeter 204; (iii)locations 618 in outer zone 214 that are ‘substantially on’ inner zoneperimeter 204; (iv) locations 622 in the interior of the ‘interior’ ofouter zone 214 (i.e. away from both inner zone and outer zone perimeters204, 208); (iv) locations 626 in outer zone 214 that are ‘substantiallyon’ outer zone perimeter 208; (v) locations 626 outside of outer zone214 that are ‘substantially on’ outer zone perimeter 208.

For each candidate location 614 in inner zone 210 that is ‘substantiallyon’ inner zone perimeter 204, a ratio between (i) a distance from thecandidate location 614 to a nearest location on inner zone perimeter 204and (ii) a distance from the candidate location 614 to a centroid ofinner zone 210 (i.e. the area enclosed by inner zone perimeter 204) isat most 0.25 or at most 0.2 or at most 0.15 or at most 0.05.

For each candidate location 618 in outer zone 214 that is ‘substantiallyon’ inner zone perimeter 204, a ratio between a (i) distance from thecandidate location 618 to a nearest location on inner zone perimeter 204and (ii) a distance from the candidate location 618 to a nearestlocation on outer zone perimeter 208 is at most 0.25 or at most 0.2 orat most 0.15 or at most 0.05.

For each candidate location 626 in outer zone 214 that is substantiallyon outer zone perimeter 208, a ratio between (i) a distance from thecandidate location 626 a nearest location on outer zone perimeter 208and (ii) a distance from the candidate location 626 to a nearestlocation on inner zone perimeter 204 is at most 0.25 or at most 0.2 orat most 0.15 or at most 0.05.

For each candidate location 630 outside of outer zone perimeter 208 thatis substantially on outer zone perimeter 208, a ratio between (i) adistance from the candidate location 630 a nearest location on outerzone perimeter 208 and (ii) a distance from the candidate location 630to a centroid 298 of the area enclosed by outer zone perimeter 208 is atmost 1.25 or at most 1.15 or at most 1.05.

Reference is now made to FIG. 26A-26B. As noted above, when heaters ‘aredistributed’ around perimeter 208 of outer zone 214, this means thatheaters (i.e. which are located on or near outer zone perimeter 208) arepresent on every 90 degree sector of outer zone perimeter 208.

This is illustrated in FIGS. 26A-26B. In FIG. 26A, it is possible todivide the cross-area of the subsurface formation into four ‘quadrants’corresponding to four 90 degree sectors (i.e. since the quotient of 360degrees and four is 90 degrees) relative to any arbitrary ‘reference ray316’ starting at centroid of outer zone 214. FIGS. 26A-26B illustraterespective orientations of reference ray 316.

After the orientation of reference ray 316 relative to the heaterpattern is fixed, it is possible to define the cross section of thesubsurface formation, relative to ray 316, into four quadrants Q1 160,Q2 162, Q3 164, and Q4 166. Dividing the subsurface formation into fourquadrants also divides outer perimeter 208 into four portions—in FIG.26A, these four portions are defined as (i) the portion of outer zoneperimeter 208 located in Q1 160 between points 402 and 404; (ii) theportion of outer zone perimeter 208 located in Q2 162 between points 402and 408; (iii) the portion of outer zone perimeter 208 located in Q3 164between points 406 and 408; (iv) the portion of outer zone perimeter 208located in Q4 166 between points 406 and 404. Thus, in FIG. 26A, thesefour portions are determined by four points on outer zone perimeter 208,namely points 402, 404, 406 and 408. In FIG. 26B associated with adifferent orientation of reference ray 316, these four portions aredetermined by points 422, 424, 426 and 428, all lying on outer zoneperimeter 208.

For the present disclosure, when heaters are ‘present’ on every 90degree sector of outer zone perimeter 208, then irrespective of anorientation of a reference line 316 relative to which four quadrants aredefined (i.e. for any arbitrary reference line orientation), there is atleast one outer perimeter heater 236 within each of the four quadrants.This concept can be generalized to 72 degree sectors (i.e. to divide thesubsurface cross section into five equal portions rather than fourquadrants), 60 degrees sectors (i.e. six equal portions or ‘sextants’)and 45 degree sectors (i.e. eight equal portions or ‘octants’).

Reference is now made to FIGS. 27-28.

Embodiments of the present invention relate to features of ‘distancesbetween heaters’ or ‘distances between a heater and a location,’ where‘distance’ and ‘displacement’ may be used interchangeably. As notedabove, unless indicated otherwise, any ‘distance’ or ‘displacement’refers to a distance or displacement constrained within atwo-dimensional cross section for which a heater pattern is defined—forexample, including but not limited to any heater pattern illustrated inFIGS. 2-11 and 15-16.

In particular, embodiments of the present invention relate to apparatusand methods whereby (i) due to the relatively ‘high’ heater density andto the distribution of inner zone heaters 226 throughout inner zone 210,a significant fraction of inner zone 210 is ‘very close’ to a nearestheater; (ii) due to the relatively ‘low’ heater density and to featurewhereby most outer zone heaters 228 are arranged at or near outerperimeter 208, a significantly smaller fraction of outer zone 214 is‘very close’ to a nearest heater. As such, the rate of productionincreases in the inner zone 210 significantly faster than in the outerzone 214.

Referring to FIGS. 27-28, it is noted that a ‘distance between heaters’refers to the distance between respective heater centroids. Unlessindicated otherwise, a ‘heater centroid’ 310 is a centroid of the heatercross-section co-planar the two-dimensional cross-section of thesubsurface where any heater pattern feature is defined. As evidenced byFIGS. 27A-27B, heater cross-section is not required to be circular. Asevidenced by FIGS. 27A-27B, the ‘distance between heaters 220,’ which isthe distance between their respective centroids 310, is not necessarilybetween the locations on the heater surface.

Some embodiments refer to a ‘distance’ or ‘displacement’ between alocation (indicated in FIGS. 28A-28D by an ‘X’) within the subsurfaceformation and one of the heaters. Unless indicated otherwise, this‘distance’ or ‘displacement’ is: (i) the distance D within the planedefined by the two-dimensional cross-section of the subsurface where anyheater pattern feature is defined; (ii) the distance D between thelocation ‘X’ and the heater centroid 310. In the examples of FIGS. 28Aand 28B, the distance between a location ‘X’ and heater 220, is definedby the distance between heater centroid 310 and location ‘X,’ even forsituations where the location ‘X’ is within heater 220 but displacedfrom heater centroid 310.

FIGS. 29A-29C illustrate the concept of a substantially convex shape. Ifa candidate shape 720 is convex it is, by definition, also substantiallyconvex. If candidate shape 720 is not convex, it is possible todetermine if candidate shape 720 is substantially convex according toone of two theoretical convex shapes: (i) a minimum-area enclosingconvex shape 722—i.e. the smallest (i.e. of minimum area) convex shapewhich completely encloses the candidate shape 720; (ii) a maximum-areaenclosed convex shape 724—i.e. the ‘largest’ (i.e. of maximum area)convex shape which is completely within candidate shape 720

It is possible to define a first area ratio as a ratio between (i) anarea enclosed by minimal-area enclosing convex shape 722 and (ii) anarea enclosed by candidate shape 720. It is possible to define a secondarea ratio as a ratio between (i) an area enclosed by candidate shape720 and (ii) an area enclosed by maximum-area enclosed convex shape 724.

For the present disclosure, a candidate shape 720 is ‘substantiallyconvex’ if one or both of these area ratios is at most a ‘thresholdvalue.’ Unless specified otherwise, this threshold value is at most 1.3.In some embodiments, this threshold value may be at most 1.2 or at most1.15 or at most 1.1 or at most 1.05.

If one or both of these area ratios is at most a value X, ‘convex shapetolerance value’ of the candidate shape 720 is said to be X. Thus, asnoted in the previous paragraphs, in different embodiments, the ‘convexshape tolerance value’ is at most 1.2 or at most 1.15 or at most 1.1 orat most 1.05.

As noted above, for the present disclosure, ‘spatial heater density’ isdefined according to the principles of reservoir engineering. Forexample, the heater FIG. 2A, nineteen heaters are inner zone heaters 226located on the inner zone perimeter 204 or within inner zone 210, whiletwelve heaters are outer zone heaters 228 located on outer zoneperimeter 208 or within outer zone 214.

FIG. 30 illustrates a portion of the heater scheme of FIG. 2A, whereheaters are labeled as in FIG. 22C. For density purposes, it is possibleto draw an ‘immediate-neighboring-region circle’ around each heatercentroid (i.e. serving as a heater ‘locator point’ within across-section of the subsurface formation in which the heater (well)pattern is defined) having a circle radius equal to one-half of adistance to a nearest neighboring heater.

In the example of FIG. 30, the radius of immediate-neighboring-regioncircles around heaters 220A, 220C and 220G, 220E and 220G (i.e. alllocated on vertices of outer hexagon 208) equals a, the radius ofimmediate-neighboring-region circles around heaters 220B, 220D and 220F(i.e. all located halfway between adjacent vertices of outer hexagon208) is

${\frac{\sqrt{3}}{2}a},$

and the radius of immediate-neighboring-region circles around inner zoneheaters 220H-220P is

$\frac{a}{2}.$

For the heater pattern scheme of FIG. 2A, ‘outer-hexagon-vertex’ heaters(see, for example, the outer zone heaters labeled as 220A, 220C, 220Eand 220G in FIG. 30) are outer zone heaters are located on vertices ofouter hexagon 208, ‘outer-hexagon-mid-side’ heaters (see, for example,the outer zone heaters labeled as 220B, 220D and 220F in FIG. 30) areouter zone heaters located midway between adjacent vertices of outerhexagon 208, ‘inner-hexagon-vertex’ heaters (see, for example, the innerzone heaters labeled as 220H, 220J, 220L and 220N in FIG. 30) are innerzone heaters are located on vertices of inner hexagon 204, and‘inner-hexagon-mid-side’ heaters (see, for example, the outer zoneheaters labeled as 220I, 220K and 220M in FIG. 30) are inner zoneheaters located midway between adjacent vertices of inner hexagon 204.

Exactly one-third of the area enclosed by respectiveimmediate-neighboring-region circles centered at ‘outer-hexagon-vertex’heaters is within outer zone 214. Thus, it may be said that one-third ofeach of these heaters ‘belong’ to outer zone 214, and two-thirds of eachof these heaters ‘belong’ to the region outside of outer zone 214 (i.e.not enclosed by outer zone perimeter 208).

Exactly one-half of the area enclosed by respectiveimmediate-neighboring-region circles centered at‘outer-hexagon-mid-side’ heaters is within outer zone 214. Thus, it maybe said that one-half of each of these heaters ‘belong’ to outer zone214, and one-half of each of these heaters ‘belong’ to the regionoutside of outer zone 214 (i.e. not enclosed by outer zone perimeter208).

Exactly one-third of the area enclosed by respectiveimmediate-neighboring-region circles centered at ‘inner-hexagon-vertex’heaters is within inner zone 214. Thus, it may be said that one-third ofeach of these heaters ‘belong’ to inner zone 210, and two-thirds of eachof these heaters ‘belong’ to outer zone 214.

Exactly one-half of the area enclosed by respectiveimmediate-neighboring-region circles centered at‘inner-hexagon-mid-side’ heaters is within inner zone 210, and exactlyone-half of the area is within outer zone 214. Thus, it may be said thatone-half of each of these heaters ‘belong’ to outer zone 214, andone-half of each of these heaters ‘belong’ to inner zone 210 (i.e. notenclosed by outer zone perimeter 208).

For the heater pattern of FIG. 2A, for the purposes of computing heaterspatial density, the total number of heaters ‘belonging to’ inner zone210 include: (i) seven ‘internally-located’ heaters 226 located withininner zone 210 and not on the perimeter of inner hexagon 204 (i.e.including heaters 220O and 220P); (ii) one-half of each of the six innerzone heaters 226 located midway between adjacent vertices of the innerhexagon 204 (i.e. including heaters 220I, 220K and 220M) for a total ofthree heaters; and (iii) one-third of each of the six inner zone heaters226 located at vertices of the inner hexagon 204 (i.e. including heaters220H, 220J, 220L and 220N) for a total of two heaters. Thus, a total of7+3+2=12 heaters belong to inner zone 210 for the purposes of computingheater spatial density.

For the heater pattern of FIG. 2A, for the purposes of computing heaterspatial density, the total number of heaters ‘belonging to’ outer zone214 include: (i) one-half of each of the six inner zone heaters 226located midway between adjacent vertices of the inner hexagon 204 (i.e.including heaters 220I, 220K and 220M) for a total of three heaters;(ii) two-thirds of each of the six inner zone heaters 226 located atvertices of the inner hexagon 204 (i.e. including heaters 220H, 220J,220L and 220N) for a total of four heaters; (iii) one-half of each ofthe six outer zone heaters 228 located midway between adjacent verticesof the outer hexagon 208 (i.e. including heaters 220B, 220D and 220F)for a total of three heaters; and (iv) one-third of each of the sixouter zone heaters 228 located at vertices of the outer hexagon 208(i.e. including heaters 220A, 220C, 220E and 220G) for a total of twoheaters. Thus, it may be said that a total of 3+4+3+2=12 heaters belongto outer zone 214 for the purposes of computing heater spatial density.

In the example of FIG. 2A, 12 heaters belong to inner zone 210 and 12heaters belong to outer zone 214. Because the area of outer zone 214 isthree times that of inner zone 210, because the number of heatersbelonging to inner 210 and outer 214 zones is the same, the heaterspatial density within inner zone 210 may be said to be three times thatof outer zone 214.

In general, to compute a ‘heater spatial density’ of any given region(i.e. cross section of the subsurface), one (i) determines, for eachheater in the formation within or relatively close to the given region,a nearest neighboring heater distance; (ii) for each heater, determinesa ‘immediate-neighboring-region circle’ around each heater centroid(i.e. having a radius equal to one half of the distance to a nearestneighboring heater), (iii) computes, for each heater in the formation, afraction of the immediate-neighboring-region circle located within thegiven region to determine the fraction (i.e. between 0 and 1) of theheater belonging to the given region; (iv) determines the total numberof heaters belonging to the given region and (v) divides this number bythe area of the given region.

In the example of FIG. 4A, exactly 16 heaters belong to inner zone 210and exactly 16 heaters ‘belong to’ outer zone 214. Thus, in the exampleof FIG. 4A, a ratio between (i) a heater spatial density in inner zone210; and (ii) a heater spatial density in outer zone 214, is exactlythree.

In different embodiments, a spatial density ratio between a heaterspatial density in inner zone 210 and that of outer zone 214 is at least1.5, or at least 2, or at least 2.5 and/or at most 10 or at most 7.5 orat most 5 or at most 4.

Some embodiments relate to a ‘nearest heater’ to a location in thesubsurface formation. In the example of FIG. 31, location A 2242 (markedwith a star) is closer to heater ‘A’ 2246 than to any other heater.Therefore, a ‘distance to a nearest heater at location A’ is thedistance between location ‘A’ 2242 and heater ‘A’ 2246. In the exampleof FIG. 31, location B 2252 (marked with a cross) is closer to heater‘B’ 256 than to any other heater. Therefore, a ‘distance to a nearestheater at location B’ is the distance between location B 2252 and heaterB 2256. In the example of FIG. 31, location C 2262 (marked with a numbersymbol) is closer to heater ‘C’ 2266 than to any other heater.Therefore, a ‘distance to a nearest heater at location C’ is thedistance between location C 2262 and heater C 2266.

In the example of FIG. 32, exactly two heaters are arranged so that‘Heater P’ 2102 is located at point (0,1) and ‘Heater Q’ 2104 is locatedat point (2,1). As such, all locations within region ‘K’ 2106 are closerto heater ‘P’ 2102 than to heater ‘Q’ 2104, and locations within region‘L’ 2108 are closer to heater ‘Q’ 2104 than to heater ‘P’ 2102.Locations on the boundary between regions ‘K’ 2106 and ‘L’ 2108 areequidistant to the heaters.

Some embodiments relate to the ‘average distance’ within an area of thesubsurface formation or on a curve within the surface formation (e.g. aclosed curve such as a zone perimeter 204 or 208 or 202) to a nearestheater. Each location within the area of curve LOCεAREA or LOCεCURVE isassociated with a distance to a nearest heater (or heater well)—this isthe distance within the cross-section of the subsurface formation forwhich a heater pattern is defined to a heater centroid within thecross-section (see FIGS. 27-28). The heater which is the ‘nearestheater’ to the location LOC E AREA or LOC E CURVE within the area or onthe curve is not required to be located in the ‘area’ AREA or curve.

Strictly speaking, an area or curve of the subsurface of formation is alocus of points. Each given point of the locus is associated with arespective distance value describing a distance to a heater closest tothe given point. By averaging these values over all points in the areaor on the curve it is possible to compute an average distance, withinthe area or on the curve, to a nearest heater.

FIGS. 33-36 illustrate some relatively simple examples.

FIG. 33A illustrates a (i) single heater A 2090 situated at the origin,and (ii) Region A 2032 which is bounded by the lines x=0, x=1, y=0, y=1.In the example of FIG. 33A, for any point (x₀,y₀) within Region A 2032,a distance to a nearest heater is the same as the distance to theorigin, i.e. √{square root over ((x₀)²+(y₀)²)}{square root over((x₀)²+(y₀)²)}. In order to determine the average distance within RegionA to a nearest heater, it is possible to compute the integral:

$\begin{matrix}{\frac{\int_{{Region}\_ A}{\sqrt{\left( x_{0} \right)^{2} + \left( y_{0} \right)^{2}}\ {x}{y}}}{{{Area\_ of}{\_ Region}{\_ A}}} = {\frac{\int_{y = 0}^{1}{\int_{x = 0}^{1}{\sqrt{\left( x_{0} \right)^{2} + \left( y_{0} \right)^{2}}\ {x}\ {y}}}}{\int_{y = 0}^{1}{\int_{x = 0}^{1}{{x}\ {y}}}} = {{{\frac{1}{6}{\ln \left( {1 + \sqrt{2}} \right)}} + \frac{\sqrt{2}}{3} - {\frac{1}{12}{arc}\; \tan \; {h\left( \frac{\sqrt{2}}{2} \right)}} - {\frac{1}{4}{\ln \left( {\sqrt{2} - 1} \right)}}} \approx 0.765}}} & \left( {{EQN}\mspace{14mu} 2} \right)\end{matrix}$

The ‘average distance to a nearest heater’ within Region A (i.e. in thiscase, a distance to heater A 2090 situated at the original) may beapproximated by a distance between (i) a centroid of Region A 2032—i.e.the point (½,1/2); and (ii) heater A 2090. This distance is equal toapproximately 0.71.

EQN. 2 is valid for a particular region illustrated in FIG. 33A. For anyarbitrary REGION of the subsurface, an entirety of which is nearer toHEATER_H than to any other heater, the average distance to a nearestheater or AVG_NHD (NHD is an abbreviation for ‘nearest heater distance’)is given by:

$\begin{matrix}{{{AVG\_ NHD}({REGION})} = \frac{\int_{REGION}{{{DIST}\left( {{LOC},{HEATER\_ H}} \right)}\ {{LOC}}}}{{{Area\_ of}{\_ REGION}}}} & \left( {{EQN}\mspace{14mu} 3} \right)\end{matrix}$

where LOC is a location within REGION, dLOC is the size (i.e. area orvolume) of an infinitesimal portion of the subsurface formation atlocation LOC within REGION, and DIST(LOC,HEATER_H) is a distance betweenHEATER_H and location LOC.

In the example of FIG. 33 only a single heater is present—i.e. Heater A2090 situated at the origin. Region B 2032 of FIG. 33B is bounded by thelines x=0, x=0.5, y=0, y=1. For the example of FIG. 18B, EQN 2 yieldsAVG_NHD((Region B)=0.59. This may be approximated by a distance betweena centroid of Region B and Heater A 2090, or 0.56.

EQN. 3 assumes that only a single heater is present in the subsurfaceformation. EQN. 3 may be generalized for a subsurface in which a heaters{H₁, H₂, . . . H_(i) . . . H_(N)} (i.e. for any positive integer N) arearranged at respective locations {LOC(H₁), LOC(H₁), . . . LOC(H_(i)), .. . LOC(H_(N)),}. In this situation, any location LOC within thesubsurface formation is associated with a respective nearest heaterH_(NEAREST)(LOC) that is selected from {H₁, H₂, . . . H_(i) . . .H_(N)}. In the example of FIG. 32, for all locations within Region K2106, a nearest heater H_(NEAREST)(LOC) is Heater P 2102 situated at(0,1). In the example of FIG. 6, for all locations within Region L 2108,a nearest heater H_(NEAREST)(LOC) is Heater Q 2104 situated at (2,1).

For location LOC within the subsurface formation, a nearest heaterdistance NHD(LOC) is defined as DIST(LOC, H_(NEAREST)(LOC))—a distancebetween the location LOC and its associated nearest heaterH_(NEAREST)(LOC). Thus, EQN. 3 may be generalized as:

$\begin{matrix}{{{AVG\_ NHD}({REGION})} = {\frac{\int_{REGION}{{{NHD}({LOC})}\ {{LOC}}}}{{{Area\_ of}{\_ REGION}}}.}} & \left( {{EQN}\mspace{14mu} 4} \right)\end{matrix}$

For the example of FIG. 20, four heaters are arranged in the subsurfaceformation—Heater A 90 situated at the origin, Heater B 2092 situated at(0,2), Heater C 2094 situated at (2,2) and Heater D 2096 situated at(2,0). In this example, it is desired to compute the average heaterdistance within Region C 2036 defined by all locations enclosed by thefour lines x=0, x=2, y=0, y=2. Region C 36 may be divided into foursub-regions A1-A4 2080, 2082, 2084, 2086. For any location LOC_(A1) insub-region A1 2080, a nearest heater H_(NEAREST)(LOC_(A1)) is Heater B2092. For any location LOC_(A3) in sub-region A3 2084, a nearest heaterH_(NEAREST)(LOC_(A3)) is Heater A 90. For any location LOC_(A2) insub-region A2 2082, a nearest heater H_(NEAREST)(LOC_(A2)) is Heater C2094. For any location LOC_(A4) in sub-region A4 2060, a nearest heaterH_(NEAREST)(LOC_(A4)) is Heater D 2096.

By symmetry, it is clear that the average distance to a nearest heaterwithin Region C 2036 AVG_NHD(REGION C) of FIG. 34 is identical to theaverage distance to a nearest heater within Region A 2032 AVG_NHD(REGIONA) of FIG. 33A, or 0.765.

For the example of FIG. 35A, five heaters are arranged in the subsurfaceformation—Heater A 2090 situated at the origin, Heater B 2092 situatedat (0,2), Heater C 2094 situated at (2,2), Heater D 2096 situated at(2,0) and Heater E 2098 situated at (1,1). In this example, it isdesired to compute the average heater distance within Region C 2036defined by all locations enclosed by the four lines x=0, x=2, y=0, y=2.Region C 2036 may be divided into eight sub-regions B1-B8 2060, 2062,2064, 2066, 2068, 2072, 2074. For any location LOC_(B1) in sub-region B12060, a ‘nearest heater’ H_(NEAREST)(LOC_(B1)) is Heater B 2092. For anylocation LOC_(B2) in sub-region B2 2062, a ‘nearest heater’H_(NEAREST)(LOC_(B2)) is Heater E 2098. For any location LOC_(B3) insub-region B3 2064, a ‘nearest heater’ H_(NEAREST)(LOC_(B3)) is Heater E2098. For any location LOC_(B4) in sub-region B4 2066, a ‘nearestheater’ H_(NEAREST)(LOC_(B4)) is Heater C 2094.

For any location LOC_(B5) in sub-region B5 2068, a nearest heaterH_(NEAREST)(LOC_(B5)) is Heater A 2090. For any location LOC_(B6) insub-region B6 70, a nearest heater H_(NEAREST)(LOC_(B6)) is Heater E2098. For any location LOC_(B7) in sub-region B7 2072, a nearest heaterH_(NEAREST)(LOC_(B7)) is Heater E 2098. For any location LOC_(B8) insub-region B8 2074, a nearest heater H_(NEAREST)(LOC_(B8)) is Heater D2096.

By symmetry, it is clear that the average distance to a nearest heaterwithin Region C 2036 AVG_NHD(REGION C) of FIG. 35A is identical to theaverage distance to a nearest heater within Region B 2034 AVG_NHD(REGIONB) of FIG. 33B, or 0.59.

In the example of FIG. 35A, there are four corner heaters and a fifthmore central heater E 2098 situated exactly in the center of thesquare-shaped region. In the example of FIG. 35B, there are also fourcorner heaters—however, the fifth more central heater E′ 98′ is situatedon the center of one of the square sides rather than in the center ofthe square. The heater density for both the example of 35A and of 35B isidentical. However, the ‘average distance to a nearest heater’ in theexample of FIG. 35B is about 0.68, or about 15% greater than that of theexample of FIG. 35A. This is due to the less uniform distribution ofheaters within Region C 2038 in the example of FIG. 35B.

The aforementioned examples relate to the average distance to a nearestheater within an area of the sub-formation formation. It is alsopossible to compute the ‘average distance to a nearest heater’ for anyset of points—for example, along a line, or along a curve, or along theperimeter of a polygon.

In the example of FIG. 36 (i.e. in this example, exactly one heater issituated in the subsurface formation), the ‘average distance to anearest heater’ along the perimeter 2052 of region A 2032 is given by:

                                       (EQN.  5)$\frac{{\int_{0}^{1}{y\ {y}}} + {\int_{x = 0}^{1}{\sqrt{(x)^{2} + 1}\ {x}}} + {\int_{y = 0}^{1}{\sqrt{(y)^{2} + 1}\ {y}}} + {\int_{0}^{1}{x{x}}}}{4} = {\frac{{\int_{x = 0}^{1}{\sqrt{(x)^{2} + 1}\ {x}}} + {\int_{0}^{1}{x{x}}}}{2} \approx 1.15}$

In general, for a curve (e.g. a closed curve) C, the average distance toa nearest heater

$\begin{matrix}{{{AVG\_ NHD}\left( {{ALONG\_ CURVE}{\_ C}} \right)} = \frac{\int_{{CURVE}\_ C}{{{NHD}({LOC})}\ {{LOC}}}}{{{Length\_ of}{\_ Curve}{\_ C}}}} & \left( {{EQN}.\mspace{14mu} 6} \right)\end{matrix}$

where location LOC is a location on Curve C. One example of a Curve isinner zone or outer zone perimeters 204, 208.

FIG. 37A illustrates fractions of inner 210 and outer 214 zones (andperimeters 204, 208 thereof) that are heater-displaced orheater-centroid-displaced by at most a first threshold distance;diam₁/2. Diam₁ is the diameter of a circle centered around each heatercentroid 310. Shaded locations in FIG. 8 are those portions of inner andouter zones which are displaced from a centroid 310 of one or more ofthe heaters 210 by less than a distance Diam₁. In the example of FIG.15, each shaded circle has an area that is around 3-5% of the area ofinner zone 210.

Because a significant number of heaters are located throughout innerzone 210, the fraction of inner zone 210 that is shaded issignificant—e.g. at least 30% or at least 40% or at least 50% or atleast 60% or at least 70% of the area of inner zone 210. Because asignificant number of heaters are located around an entirety of innerperimeter 204, the fraction of inner perimeter 204 that is shaded issignificant—e.g. at least 30% or at least 40% or at least 50% or atleast 60% or at least 70% of the length of inner perimeter 204. Incontrast, due to the much lower heater density in outer zone 210, a muchsmaller fraction of outer zone 210 is shaded.

In the example of FIG. 37B, it is shown that when the threshold distanceis increased from a first to a second threshold distance, the portion ofthe outer perimeter 208 that is heater-displaced or‘heater-centroid-displaced’ by at most the second threshold distance issignificant—e.g. at least 30% or at least 40% or at least 50% or atleast 60% or at least 70% of the length of outer perimeter 208.

In one example, the area of the circle defining locations (e.g. see theshaded circles of FIG. 37A) within the subsurface formation (i.e. in theplane in which a heater pattern is defined) is exactly 5% of the area ofinner zone 210. In this case, the radius of inner zone 210 equals

$\sqrt{\frac{0.05}{\pi}}$

or about 12.6% (or about one-eighth) of the square root of the area ofinner zone 210, where the square root of the area of inner zone 210 hasdimensions of length.

Embodiments of the present invention relate to apparatus and methodswhereby, for a cross-section of the subsurface formation, and for athreshold length or threshold distance that is equal to one-eighth ofthe area of inner zone 204, (i) a significant fraction of inner zone 210is covered by the shaded circles having a radius equal to the thresholddistance and an area equal to about 5% of the area of inner zone 204;(ii) only a significantly smaller fraction of outer zone 214 is coveredby the shaded circles having a radius equal to the same thresholddistance, due to the much lower heater density. In some embodiments, asignificant fraction of the length of inner perimeter 204 is covered byshaded circles. In some embodiments, for a second threshold distanceequal to twice the aforementioned ‘threshold distance’ (e.g. equal toone quarter of the square root of the area of inner zone 210), a‘significant fraction’ of the length of outer perimeter 208 is coveredby shaded circles.

In one example, it is possible to set a threshold distance or thresholdlength to one-eighth of the area of inner zone 204 so that a magnitudeof an area enclosed by a circle whose radius is the ‘threshold distance’is equal to 5% of that of the inner zone 204.

According to this threshold distance, for the heater patternsillustrated in FIG. 5A, (i) more than 50% (for example, about 60%) ofinner zone 210 is heater-displaced or teater-centroid-displaced by lessthan this threshold distance, and (ii) a much smaller fraction, i.e.about 15-20% of outer zone 214 is displaced by less than this thresholddistance. For the example of FIG. 3A, according to this thresholddistance, (i) well over two-thirds of inner zone 210 is heater-displacedor heater-centroid displaced by less than this threshold distance; and(ii) a much smaller fraction, about a third, of outer zone 210 isheater-displaced by less than this threshold distance.

In both examples, a ratio between (i) a fraction of inner zone 210 thatis heater-displaced or heater-centroid displaced by at most thethreshold distance; and (ii) a fraction of outer zone 214 that isheater-displaced or heater-centroid displaced by at most the thresholddistance is at least 1.2 or at least 1.25 or at least 1.3 or at least1.4 or at least 1.5 or at least 1.6 or at least 1.8 or at least 1.9.

In the example of FIG. 37A, about 60% of a length of inner perimeter 204is heater-displaced or heater-centroid-displaced by at most thisthreshold distance and about 60% of a length of outer perimeter 208 isheater-displaced or heater-centroid-displaced by at most twice thisthreshold distance. In some embodiments, over 75% of a length of innerperimeter 204 is heater-displaced or heater-centroid-displaced by atmost this threshold distance and over 75% of a length of outer perimeter208 is heater-displaced or heater-centroid-displaced by at most twicethis threshold distance.

Embodiments of the present invention refer to ‘control apparatus.’Control apparatus may include any combination of analog or digitalcircuitry (e.g. current or voltage or electrical power regulator(s) orelectronic timing circuitry) and/or computer-executable code and/ormechanical apparatus (e.g. flow regulator(s) or pressure regulator(s) orvalve(s) or temperature regulator(s)) or any monitoring devices (e.g.for measuring temperature or pressure) and/or other apparatus.

Some embodiments relate to patterns of heaters and/or production wellsand/or injection wells.

Some embodiments relate to methods of hydrocarbon fluid productionand/or methods of heating a subsurface formation. Unless specifiedotherwise, any feature or combination of feature(s) relating to heaterand/or production well locations or patterns may be provided incombination with any method disclosed herein even if not explicitlyspecified herein. Furthermore, a number of methods are disclosed withinthe present disclosure, each providing its own set of respectivefeatures. Unless specified otherwise, in some embodiments, anyfeature(s) of any one method may be combined with feature(s) of anyother method, even if not explicitly specified herein.

Furthermore, any ‘control apparatus’ may be programmed to carry out anymethod or combination thereof disclosed herein.

In the description and claims of the present application, each of theverbs, “comprise” “include” and “have”, and conjugates thereof, are usedto indicate that the object or objects of the verb are not necessarily acomplete listing of members, components, elements or parts of thesubject or subjects of the verb.

All references cited herein (including but not limited to PCT/US13/38089filed on Apr. 24, 2013 and U.S. 61/729,628 filed on Nov. 25, 2012) areeach incorporated by reference in their entirety. Citation of areference does not constitute an admission that the reference is priorart.

The articles “a” and “an” are used herein to refer to one or to morethan one. (i.e, to at least one) of the grammatical object of thearticle. By way of example, “an element” means one element or more thanone element.

The term “including” is used herein to mean, and is used interchangeablywith, the phrase “including but not limited” to.

The term “or” is used herein to mean, and is used interchangeably with,the term “and/or,” unless context clearly indicates otherwise.

The term “such as” is used herein to mean, and is used interchangeably,with the phrase “such as but not limited to”.

The present invention has been described using detailed descriptions ofembodiments thereof that are provided by way of example and are notintended to limit the scope of the invention. The described embodimentscomprise different features, not all of which are required in allembodiments of the invention. Some embodiments of the present inventionutilize only some of the features or possible combinations of thefeatures. Variations of embodiments of the present invention that aredescribed and embodiments of the present invention comprising differentcombinations of features noted in the described embodiments will occurto persons skilled in the art.

What is claimed is:
 1. A system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that an average heater spacing in outer zonesignificantly exceeds that of inner zone, at least a majority of theheaters in the inner zone being powered primarily by fuel combustion andat least a majority of heaters in the outer zone being powered primarilyby electricity generated by wind.
 2. A system for in-situ production ofhydrocarbon fluids from a subsurface hydrocarbon-containing formation,the system comprising: a heater cell divided into nested inner and outerzones such that an enclosed area ratio between respective areas enclosedby substantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that an average heater spacing in outer zonesignificantly exceeds that of inner zone, at least a majority of theheaters in the inner zone being powered primarily by fuel combustion andat least a majority of heaters in the outer zone being powered primarilyby electricity generated by wind.
 3. A system for in-situ production ofhydrocarbon fluids from a subsurface hydrocarbon-containing formation,the system comprising: a heater cell divided into nested inner and outerzones such that an enclosed area ratio between respective areas enclosedby substantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that a heater spatial density in inner zone significantlyexceeds that of outer zone, at least a majority of the heaters in theinner zone being powered primarily by fuel combustion and at least amajority of heaters in the outer zone being powered primarily byelectricity generated by wind.
 4. A system for in-situ production ofhydrocarbon fluids from a subsurface hydrocarbon-containing formation,the system comprising: heaters arranged in a target portion of theformation, the target portion being divided into nested inner and outerzones heaters so that inner zone and outer zone heaters are respectivelydistributed around inner and outer zone centroids, at least a majorityof the heaters in the inner zone being powered primarily by fuelcombustion and at least a majority of heaters in the outer zone beingpowered primarily by electricity generated by wind.
 5. A system forin-situ production of hydrocarbon fluids from a subsurface formation,the system comprising: (i) heaters powered primarily by fuel combustionand (ii) heaters powered primarily by electricity generated by windarranged within a target portion of the sub-surface formation.
 6. Thesystem of any previous claim wherein, within the target formation, afirst heater that is powered primarily by fuel combustion is located atmost 50 meters from a second heater that is powered primarily byelectricity generated by wind.
 7. The system of any previous claimwherein, within the target formation, a first heater that is poweredprimarily by fuel combustion is located at most 35 meters from a secondheater that is powered primarily by electricity generated by wind. 8.The system of any previous claim wherein, within the target formation, afirst heater that is powered primarily by fuel combustion is located atmost 20 meters from a second heater that is powered primarily byelectricity generated by wind.
 9. The system of any previous claimwherein, within the target formation, a first heater that is poweredprimarily by fuel combustion is located at most 10 meters from a secondheater that is powered primarily by electricity generated by wind. 10.The system of any previous claim wherein, within the target formation, afirst heater that is powered primarily by fuel combustion is located atmost 5 meters from a second heater that is powered primarily byelectricity generated by wind.
 11. The system of any previous claimwherein, within the target formation, the average separation distancebetween neighboring heaters that are each powered primarily byelectricity generated by wind exceeds the average separation distancebetween neighboring heaters that are each powered primarily by fuelcombustion.
 12. The system of any previous claim wherein, within thetarget formation, the average separation distance between neighboringheaters that are each powered primarily by electricity generated by windsignificantly exceeds the average separation distance betweenneighboring heaters that are each powered primarily by fuel combustion.13. The system of any previous claim wherein, within the targetformation, the average separation distance between neighboring heatersthat are each powered primarily by electricity generated by windsignificantly is about twice the average separation distance betweenneighboring heaters that are each powered primarily by fuel combustion.14. The system of any of claims 5-13 wherein at least some, or at leasta majority, or at least two-thirds of the heaters powered primarily byfuel combustion are electrical heaters that are powered primarily byelectricity generated by fuel combustion.
 15. The system of any ofclaims 5-14 wherein at least some, or at least a majority, or at leasttwo-thirds of the heaters powered primarily by fuel combustion arecombustion heaters where a combusted gas is circulated in thesubsurface.
 16. The system of any of claims 5-17 wherein at least some,or at least a majority, or at least two-thirds of the heaters poweredprimarily by fuel combustion are electrical heaters wherein a materialis resistively heated by electricity generated by fuel combustion. 17.The system of any of claims 5-18 wherein at least some, or at least amajority, or at least two-thirds of the heaters powered primarily byfuel combustion are advection heaters where a material, that is inthermal communication with a circulating heat transfer fluid flowing inthe subsurface, is heated resistively by electricity generated by fuelcombustion.
 18. The system of claim 17 wherein the resistively heatedmaterial is in the subsurface.
 19. The system of claim 17 wherein theresistively heated material is above the surface.
 20. The system of anyof claims 5-19 wherein at least some, or at least a majority, or atleast two-thirds of the heaters powered primarily by electricitygenerated by wind are electrical heaters wherein a material isresistively heated by electricity generated by wind.
 21. The system ofany of claims 5-20 wherein at least some, or at least a majority, or atleast two-thirds of the heaters powered primarily by electricitygenerated by wind are advection heaters where a material, that is inthermal communication with a circulating heat transfer fluid flowing inthe subsurface, is heated resistively by electricity generated by wind.22. The system of claim 21 wherein the resistively heated material is inthe subsurface.
 23. The system of claim 21 wherein the resistivelyheated material is above the surface.
 24. The system of any of claims1-16 wherein two-thirds of the heaters in the inner zone are poweredprimarily by fuel combustion and at least two-thirds of heaters in theouter zone are powered primarily by electricity generated by wind.
 25. Amethod of in-situ production of hydrocarbon fluids in a subsurfacehydrocarbon-containing formation, the method comprising: a. during anearlier stage of production, producing hydrocarbon fluids primarily in afirst portion of the target region that is heated primarily by thermalenergy derived from combustion of fuel; and b. during a later stage ofproduction, producing hydrocarbon fluid primarily in a second portion ofthe target region that is heated primarily by thermal energy derivedfrom electricity generated by wind, wherein at least some of the thermalenergy required for hydrocarbon fluid production in the second portionof the target region is supplied by outward migration of thermal energyfrom the first portion to the second portion of the target region.
 26. Amethod of in-situ production of hydrocarbon fluids in a subsurfacehydrocarbon-containing formation, the method comprising: a. during anearlier stage of production, producing hydrocarbon fluids primarily in afirst portion of the target region that is heated primarily by thermalenergy derived from electricity generated by wind and b. during a laterstage of production, producing hydrocarbon fluid primarily in a secondportion of the target region that is heated primarily by thermal energyderived from combustion of fuel wherein at least some of the thermalenergy required for hydrocarbon fluid production in the second portionof the target region is supplied by outward migration of thermal energyfrom the first portion to the second portion of the target region.
 27. Asystem for in-situ production of hydrocarbon fluids from a subsurfacehydrocarbon-containing formation, the system comprising: a heater celldivided into nested inner and outer zones such that an enclosed arearatio between respective areas enclosed by substantially-convexpolygon-shaped perimeters of the outer and inner zones is between twoand seven, heaters being located at all polygon vertices of inner andouter zone perimeters, inner zone and outer zone heaters beingrespectively distributed around inner and outer zone centroids such thatan average heater spacing in outer zone significantly exceeds that ofinner zone, at least a majority of the heaters in the inner zone beingpowered primarily by electricity generated by wind and at least amajority of heaters in the outer zone being powered primarily by fuelcombustion.
 28. A system for in-situ production of hydrocarbon fluidsfrom a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that an average heater spacing in outer zonesignificantly exceeds that of inner zone, at least a majority of theheaters in the inner zone being powered primarily by electricitygenerated by wind and at least a majority of heaters in the outer zonebeing powered primarily by fuel combustion.
 29. A system for in-situproduction of hydrocarbon fluids from a subsurfacehydrocarbon-containing formation, the system comprising: a heater celldivided into nested inner and outer zones such that an enclosed arearatio between respective areas enclosed by substantially-convexpolygon-shaped perimeters of the outer and inner zones is between twoand seven, heaters being located at all polygon vertices of inner andouter zone perimeters, inner zone and outer zone heaters beingrespectively distributed around inner and outer zone centroids such thata heater spatial density in inner zone significantly exceeds that ofouter zone, at least a majority of the heaters in the inner zone beingpowered primarily by electricity generated by wind and at least amajority of heaters in the outer zone being powered primarily by fuelcombustion.
 30. A system for in-situ production of hydrocarbon fluidsfrom a subsurface hydrocarbon-containing formation, the systemcomprising: heaters arranged in a target portion of the formation, thetarget portion being divided into nested inner and outer zones heatersso that inner zone and outer zone heaters are respectively distributedaround inner and outer zone centroids, at least a majority of theheaters in the inner zone being powered primarily by electricitygenerated by wind and at least a majority of heaters in the outer zonebeing powered primarily by fuel combustion.
 31. The system of any ofclaims 27-30 wherein at least two-thirds of the heaters in the innerzone are powered primarily by electricity generated by wind and at leasttwo-thirds of heaters in the outer zone being powered primarily by fuelcombustion.
 32. A system for in-situ production of hydrocarbon fluidsfrom a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that an average heater spacing in outer zonesignificantly exceeds that of inner zone, at least one heater in theinner zone and/or at least one heater in the outer zone being poweredprimarily by electricity generated by wind.
 33. A system for in-situproduction of hydrocarbon fluids from a subsurfacehydrocarbon-containing formation, the system comprising: a heater celldivided into nested inner and outer zones such that an enclosed arearatio between respective areas enclosed by substantially-convexpolygon-shaped perimeters of the outer and inner zones is between twoand seven, heaters being located at all polygon vertices of inner andouter zone perimeters, inner zone and outer zone heaters beingrespectively distributed around inner and outer zone centroids such thatan average heater spacing in outer zone significantly exceeds that ofinner zone, at least one heater in the inner zone and/or at least oneheater in the outer zone being powered primarily by electricitygenerated by wind.
 34. A system for in-situ production of hydrocarbonfluids from a subsurface hydrocarbon-containing formation, the systemcomprising: a heater cell divided into nested inner and outer zones suchthat an enclosed area ratio between respective areas enclosed bysubstantially-convex polygon-shaped perimeters of the outer and innerzones is between two and seven, heaters being located at all polygonvertices of inner and outer zone perimeters, inner zone and outer zoneheaters being respectively distributed around inner and outer zonecentroids such that a heater spatial density in inner zone significantlyexceeds that of outer zone, at least one heater in the inner zone and/orat least one heater in the outer zone being powered primarily byelectricity generated by wind.
 35. The system of any previous claimwherein an area of a region enclosed by a perimeter of the outer zone isat least three times that enclosed by a perimeter of the inner zone. 36.The system of any previous claim wherein an area of a region enclosed bya perimeter of the outer zone is at most six times that enclosed by aperimeter of the inner zone.
 37. The system of any previous claimwherein an area of a region enclosed by a perimeter of the outer zone isat most five times that enclosed by a perimeter of the inner zone. 38.The system of any preceding claim wherein a heater spatial density inthe inner zone is at least about twice that of outer zone.
 39. Thesystem of any preceding claim wherein a heater spatial density in theinner zone is at least twice that of the outer zone.
 40. The system ofany preceding claim wherein a heater spatial density in the inner zoneis at least about three times that of the outer zone.
 41. Use of thesystem of any of claims 1-40 to pyrolyze kerogen or to pyrolyze bitumenof the subsurface formation.
 42. Use of the system of any of claims 1-40to mobilize bitumen of the subsurface formation.
 43. Use of the systemof any of claims 1-40 for in-situ production of hydrocarbon fluids froma subsurface hydrocarbon-containing formation.